This list of Game of Life terms is compiled by Stephen A. Silver, for which I am thankful. See the original credit page for all credits. The original Life Lexicon is available at Silver's website. This list is changed by Edwin Martin to work with the Game of Life program. His e-mail address is edwin@bitstorm.org.

This lexicon is prepared for the Game of Life program.

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:**101** (p5) Found by Achim Flammenkamp in August 1994. The name was
suggested by Bill Gosper, noting that the phase shown below
displays the period in binary.

:**1-2-3** (p3) Found by Dave Buckingham, August 1972. This is one of only
three essentially different p3 oscillators with only three cells in
the rotor. The others are stillater and cuphook.

:**1-2-3-4** (p4) See also Achim's p4.

:**14-ner** = fourteener

:**17c/45 spaceship** A spaceship travelling at 17*c*/45. No such
spaceship has actually been built, but Jason Summers has written up a
plan for making one (see http://entropymine.com/jason/life/17c45/).
The resulting spaceship would be so huge that building it without the
aid of specialized software would be practically impossible.

The design for a 17*c*/45 spaceship is based on the following
reaction between a pi-heptomino and a blinker:

:**2 eaters** = two eaters

:**4-8-12 diamond** The following pure glider generator.

:**4 boats** (p2)

:**4F** = Fast Forward Force Field

:**Achim's p144** (p144) This was found (minus the blocks shown below)
on a cylinder of width 22 by Achim Flammenkamp in July 1994. Dean
Hickerson reduced it to a finite form using figure-8s the same day.
The neater finite form shown here - replacing the figure-8s with
blocks - was found by David Bell in August 1994. See factory for
a use of this oscillator.

:**Achim's p16** (p16) Found by Achim Flammenkamp, July 1994.

:**Achim's p4** (p4) Dave Buckingham found this in a less compact form
(using two halves of sombreros) in 1976. The form shown here was
found by Achim Flammenkamp in 1988. The rotor is two copies of
the rotor of 1-2-3-4, so the oscillator is sometimes called the
"dual 1-2-3-4".

:**Achim's p5** = pseudo-barberpole

:**Achim's p8** (p8) Found by Achim Flammenkamp, July 1994.

:**acorn** (stabilizes at time 5206) A methuselah found by Charles
Corderman.

:**A for all** (p6) Found by Dean Hickerson in March 1993.

:**agar** Any pattern covering the whole plane that is periodic in both
space and time. The simplest (nonempty) agar is the stable one
extended by the known spacefillers. For some more examples see
chicken wire, houndstooth agar, onion rings, squaredance
and Venetian blinds. Tiling the plane with the pattern `O......O`
produces another interesting example: a p6 agar which has a phase of
density 3/4, which is the highest yet obtained for any phase of an
oscillating pattern.

:**aircraft carrier** (p1) This is the smallest still life that has more
than one island.

:**airforce** (p7) Found by Dave Buckingham in 1972. The rotor consists
of two copies of that used in the burloaferimeter.

:**AK47 reaction** The following reaction (found by Rich Schroeppel and
Dave Buckingham) in which a honey farm predecessor, catalysed by
an eater and a block, reappears at another location 47 generations
later, having produced a glider and a traffic light. This is the
basis of a very small (but pseudo) p94 glider gun found by Paul
Callahan in July 1994, and was in 1990 the basis for the Dean
Hickerson's construction of the first true p94 gun. (This latter
gun was enormous, and has now been superceded by comparatively small
Herschel loop guns.)

:**Al Jolson** = Jolson

:**almosymmetric** (p2) Found in 1971.

:**antlers** = moose antlers

:**ants** (p5 wick) The standard form is shown below. It is also
possible for any ant to be displaced by one or two cells relative
to either or both of its neighbouring ants. Dean Hickerson found
fenceposts for both ends of this wick in October 1992 and
February 1993. See electric fence, and also wickstretcher.

:**anvil** The following induction coil.

:**APPS** (*c*/5 orthogonally, p30) An asymmetric PPS. The same as the
SPPS, but with the two halves 15 generations out of phase with one
another. Found by Alan Hensel in May 1998.

:**ark** A pair of mutually stabilizing switch engines. The archetype
is Noah's ark.

:**arm** A long extension hanging off from the main body of a spaceship
or puffer perpendicular to the direction of travel.

A lot of known spaceships have multiple arms. This is an artefact of the search methods used to find such spaceships, rather than an indication of what a "typical" spaceship might look like.

:**ash** The (stable or oscillating) debris left by a random reaction.
Experiments show that for random soups with moderate initial
densities (say 0.25 to 0.5) the resulting ash has a density of about
0.0287. (This is, of course, based on what happens in finite fields.
In infinite fields the situation may conceivably be different in the
long run because of the effect of certain initially very rare objects
such as replicators.)

:**aVerage** (p5) Found by Dave Buckingham, 1973. The average number
of live rotor cells is five (V), which is also the period.

:**B** = B-heptomino

:**B-52 bomber** The following p104 double-barrelled glider gun.
It uses a B-heptomino and emits one glider every 52 generations.
It was found by Noam Elkies in March 1996, except that Elkies used
blockers instead of molds, the improvement being found by
David Bell later the same month.

:**babbling brook** Any oscillator whose rotor consists of a string
of cells each of which is adjacent to exactly two other rotor cells,
except for the endpoints which are adjacent to only one other rotor
cell. Compare muttering moat. Examples include the beacon, the
great on-off, the light bulb and the spark coil. The following
less trivial example (by Dean Hickerson, August 1997) is the only
one known with more than four cells in its rotor. It is p4 and has
a 6-cell rotor.

:**backrake** Another term for a backwards rake. A p8 example by
Jason Summers is shown below. See total aperiodic for a p12
example.

:**backward glider** A glider which moves at least partly in the
opposite direction to the puffer(s) or spaceship(s) under
consideration.

:**baker** (*c* p4 fuse) A fuse by Keith McClelland.

:**baker's dozen** (p12) A loaf hassled by two blocks and two
caterers. The original form (using p4 and p6 oscillators to
do the hassling) was found by Robert Wainwright in August 1989.

:**bakery** (p1) A common formation of two bi-loaves.

:**barberpole** Any p2 oscillator in the infinite sequence bipole,
tripole, quadpole, pentapole, hexapole, heptapole ...
(It wasn't my idea to suddenly change from Latin to Greek.)
This sequence of oscillators was found by the MIT group in 1970.
The term is also used (usually in the form "barber pole") to
describe other extensible sections of oscillators or spaceships,
especially those (usually of period 2) in which all generations
look alike except for a translation and/or rotation/reflection.

:**barberpole intersection** = quad

:**barber's pole** = barberpole

:**barge** (p1)

:**basic shuttle** = queen bee shuttle

:**beacon** (p2) The third most common oscillator. Found by Conway,
March 1970.

:**beacon maker** (*c* p8 fuse)

:**beehive** (p1) The second most common still life.

:**beehive and dock** (p1)

:**beehive on big table** = beehive and dock

:**beehive pusher** = hivenudger

:**beehive with tail** (p1)

:**belly spark** The spark of a MWSS or HWSS other than the
tail spark.

:**bent keys** (p3) Found by Dean Hickerson, August 1989. See also
odd keys and short keys.

:**B-heptomino** (stabilizes at time 148) This is a very common
pattern. It often arises with the cell at top left shifted one
space to the left, which does not affect the subsequent evolution.
B-heptominoes acquired particular importance in 1996 due
to Dave Buckingham's work on B tracks - see in particular
My Experience with B-heptominos in Oscillators.

:**B-heptomino shuttle** = twin bees shuttle

:**bi-block** (p1) The smallest pseudo still life.

:**bi-boat** = boat-tie

:**biclock** The following pure glider generator.

:**big beacon** = figure-8

:**big fish** = HWSS

:**big glider** (*c*/4 diagonally, p4) This was found by Dean Hickerson in
December 1989 and was the first known diagonal spaceship other than
the glider.

:**big S** (p1)

:**big table** = dock

:**billiard table configuration** Any oscillator in which the rotor
is enclosed within the stator. Examples include airforce,
cauldron, clock II, Hertz oscillator, negentropy,
pinwheel, pressure cooker and scrubber.

:**bi-loaf** This term has been used in at least three different senses.
A bi-loaf can be half a bakery:

:**bipole** (p2) The barberpole of length 2.

:**bi-pond** (p1)

:**bi-ship** = ship-tie

:**biting off more than they can chew** (p3) Found by Peter Raynham,
July 1972.

:**Black&White** = Immigration

:**blasting cap** The pi-heptomino (after the shape at generation 1).
A term used at MIT and still occasionally encountered.

:**blinker** (p2) The smallest and most common oscillator. Found by
Conway, March 1970.

:**blinker puffer** Any puffer whose output is blinkers. However,
the term is particularly used for p8 *c*/2 puffers. The first such
blinker puffer was found by Robert Wainwright in 1984, and was
unexpectedly simple:

:**blinkers bit pole** (p2) Found by Robert Wainwright, June 1977.

:**blinker ship** A growing spaceship in which the wick consists of
a line of blinkers. An example by Paul Schick based on his
Schick engine is shown below. Here the front part is p12 and
moves at *c*/2, while the back part is p26 and moves at 6*c*/13. Every
156 generations 13 blinkers are created and 12 are destroyed, so the
wick becomes one blinker longer.

:**block** (p1) The most common still life.

:**blockade** (p1) A common formation of four blocks. The final form
of lumps of muck.

:**block and dock** (p1)

:**block and glider** (stabilizes at time 106)

:**blocker** (p8) Found by Robert Wainwright. See also filter.

:**block on big table** = block and dock

:**block on table** (p1)

:**block pusher** A pattern emitting streams of gliders which can
repeatedly push a block further away. This can be used as part of a
sliding block memory.

The following pattern, in which three gliders push a block one cell diagonally, is an example of how a block puhser works.

:**blonk** A block or a blinker. This term is mainly used in the
context of sparse Life and was coined by Rich Schroeppel in
September 1992.

:**boat** (p1) The only 5-cell still life.

:**boat-bit** A binary digit represented by the presence of a
boat next to a snake (or other suitable object, such as
an aircraft carrier). The bit can be toggled by a glider
travelling along a certain path. A correctly timed glider on a
crossing path can detect whether the transition was from 1 to 0
(in which case the crossing glider is deleted) or from 0 to 1 (in
which case it passes unharmed). Three gliders therefore suffice for
a non-destructive read. The mechanisms involved are shown in the
diagram below. Here the bit is shown in state 0. It is about to
be set to 1 and then switched back to 0 again. The first crossing
glider will survive, but the second will be destroyed. (In January
1997 David Bell found a method of reading the bit while setting it
to 0. A MWSS is fired at the boat-bit. If it is already 0 then
the MWSS passes unharmed, but if it is 1 then the boat and the MWSS
are destroyed and, with the help of an eater1, converted into a
glider which travels back along exactly the same path that is used
by the gliders that toggle the boat-bit.)

:**boat maker** (*c* p4 fuse)

:**boat on boat** = boat-tie

:**boat-ship-tie** = ship tie boat

:**boatstretcher** Any wickstretcher that stretches a boat. The first
one was found by Hartmut Holzwart in June 1993. The following
example is by Noam Elkies (February 1996) and uses Tim Coe's swan.
Note that in any boatstretcher the point of the boat can be removed
to get a tubstretcher.

:**boat-tie** (p1) The name is a pun on "bow tie".

:**boojum reflector** (p1) Dave Greene's name for the following
reflector which he found in April 2001, and which is currently
the smallest known stable reflector.

:**bookend** The following induction coil. It is generation 1 of
century.

:**bookends** (p1)

:**boss** (p4) Found by Dave Buckingham, 1972.

:**bottle** (p8) Found by Achim Flammenkamp in August 1994. The name is
a back-formation from ship in a bottle.

:**bounding box** The smallest rectangular array of cells that contains
the whole of a given pattern. For oscillators and guns this
usually is meant to include all phases of the pattern, but
excludes, in the case of guns, the outgoing stream(s).

:**bow tie** = boat-tie

:**brain** (*c*/3 orthogonally, p3) Found by David Bell, May 1992.

:**breeder** Any pattern whose population grows at a quadratic rate,
although it is usual to exclude spacefillers. It is easy to see
that this is the fastest possible growth rate.

The term is also sometimes used to mean specifically the breeder created by Bill Gosper's group at MIT, which was the first known pattern exhibiting superlinear growth.

There are four basic types of breeder, known as MMM, MMS, MSM and SMM (where M=moving and S=stationary). Typically an MMM breeder is a rake puffer, an MMS breeder is a puffer producing puffers which produce stationary objects (still lifes and/or oscillators), an MSM breeder is a gun puffer and an SMM breeder is a rake gun. There are, however, less obvious variants of these types. The original breeder was of type MSM (a p64 puffer puffing p30 glider guns).

The known breeder with the smallest initial population is the metacatacryst.

:**bridge** A term used in naming certain still lifes (and the stator
part of certain oscillators). It indicates that the object
consists of two smaller objects joined edge to edge, as in
snake bridge snake.

:**broth** = soup

:**BTC** = billiard table configuration

:**B track** A track for B-heptominoes. The term is more-or-less
synonymous with Herschel track, since a B-heptomino becomes a
Herschel plus a block in twenty generations.

:**buckaroo** A queen bee shuttle stabilized at one end by an eater
in such a way that it can turn a glider, as shown below. This was
found by Dave Buckingham in the 1970s. The name is due to Bill
Gosper.

:**bullet heptomino** Generation 1 of the T-tetromino.

:**bun** The following induction coil. By itself this is a common
predecessor of the honey farm. See also cis-mirrored R-bee.

:**bunnies** (stabilizes at time 17332) This is a parent of rabbits
and was found independently by Robert Wainwright and Andrew
Trevorrow.

:**burloaf** = loaf

:**burloaferimeter** (p7) Found by Dave Buckingham in 1972. See also
airforce.

:**bushing** That part of the stator of an oscillator which is
adjacent to the rotor. Compare casing.

:**butterfly** The following pattern, or the formation of two beehives
that it evolves into after 33 generations. (Compare teardrop,
where the beehives are five cells closer together.)

:**by flops** (p2) Found by Robert Wainwright.

:**c** = speed of light

:**CA** = cellular automaton

:**caber tosser** Any pattern whose population is asymptotic to *c*.log(*t*)
for some constant *c*, and which contains a glider (or other
spaceship) bouncing between a slower receding spaceship and a
fixed reflector which emits a spaceship (in addition to the
reflected one) whenever the bouncing spaceship hits it.

As the receding spaceship gets further away the bouncing spaceship
takes longer to complete each cycle, and so the extra spaceships
emitted by the reflector are produced at increasingly large
intervals. More precisely, if *v* is the speed of the bouncing
spaceship and *u* the speed of the receding spaceship, then each
interval is (*v*+*u*)/(*v*-*u*) times as long as the previous one. The
population at time *t* is therefore *n*.log(*t*)/log((*v*+*u*)/(*v*-*u*)) + O(1),
where *n* is the population of one of the extra spaceships (assumed
constant).

The first caber tosser was built by Dean Hickerson in May 1991.

:**Cambridge pulsar CP 48-56-72** = pulsar (The numbers refer to
the populations of the three phases. The Life pulsar was indeed
discovered at Cambridge, like the first real pulsar a few years
earlier.)

:**Canada goose** (*c*/4 diagonally, p4) Found by Jason Summers, January
1999. It consists of a glider plus a tagalong.

:**candelabra** (p3) By Charles Trawick. See also the note under cap.

:**candlefrobra** (p3) Found by Robert Wainwright in November 1984.

:**canoe** (p1)

:**cap** The following induction coil. It can also be easily be
stabilized to form a p3 oscillator - see candelabra for a slight
variation on this.

:**carnival shuttle** (p12) Found by Robert Wainwright in September 1984
(using MW emulators at the end, instead of the monograms shown
here).

:**carrier** = aircraft carrier

:**casing** That part of the stator of an oscillator which is not
adjacent to the rotor. Compare bushing.

:**catacryst** A 58-cell quadratic growth pattern found by Nick Gotts
in April 2000. This was formerly the smallest known pattern with
superlinear growth, but has since been superceded by the related
metacatacryst. The catacryst consists of three arks plus a
glider-producing switch engine. It produces a block-laying switch
engine every 47616 generations. Each block-laying switch engine has
only a finite life, but the length of this life increases linearly
with each new switch engine, so that the pattern overall grows
quadratically, as an unusual type of MMS breeder.

:**catalyst** An object that participates in a reaction but emerges from
it unharmed. The term is mostly applied to still lifes, but can
also be used of oscillators, spaceships, etc. The still lifes
and oscillators which form a conduit are examples of catalysts.

:**caterer** (p3) Found by Dean Hickerson, August 1989. Compare
with jam. In terms of its minimum population of 12 this is
the smallest p3 oscillator. See also double caterer and
triple caterer.

:**Catherine wheel** = pinwheel

:**cauldron** (p8) Found in 1971 independently by Don Woods and Robert
Wainwright. Compare with Hertz oscillator.

:**cavity** = eater plug

:**cell** The fundamental unit of space in the Life universe. The term is
often used to mean a live cell - the sense is usually clear from the
context.

:**cellular automaton** A certain class of mathematical objects of which
Life is an example. A cellular automaton consists of a number of
things. First there is a positive integer *n* which is the dimension
of the cellular automaton. Then there is a finite set of states *S*,
with at least two members. A state for the whole cellular automaton
is obtained by assigning an element of *S* to each point of the
*n*-dimensional lattice Z^{n} (where Z is the set of all integers).
The points of Z^{n} are usually called cells. The cellular automaton
also has the concept of a neighbourhood. The neighbourhood *N* of the
origin is some finite (nonempty) subset of Z^{n}. The neighbourhood
of any other cell is obtained in the obvious way by translating that
of the origin. Finally there is a transition rule, which is a
function from *S*^{N} to *S* (that is to say, for each possible state of
the neighbourhood the transition rule specifies some cell state).
The state of the cellular automaton evolves in discrete time, with
the state of each cell at time *t*+1 being determined by the state
of its neighbourhood at time *t*, in accordance with the transition
rule.

There are some variations on the above definition. It is common
to require that there be a quiescent state, that is, a state such
that if the whole universe is in that state at generation 0 then it
will remain so in generation 1. (In Life the OFF state is quiescent,
but the ON state is not.) Other variations allow spaces other than
Z^{n}, neighbourhoods that vary over space and/or time, probabilistic
or other non-deterministic transistion rules, etc.

It is common for the neighbourhood of a cell to be the 3×...×3 (hyper)cube centred on that cell. (This includes those cases where the neighbourhood might more naturally be thought of as a proper subset of this cube.) This is known as the Moore neighbourhood.

:**centinal** (p100) Found by Bill Gosper. This combines the mechanisms
of the p46 and p54 shuttles (see twin bees shuttle and
p54 shuttle).

:**century** (stabilizes at time 103) This is a common pattern which
evolves into three blocks and a blinker. In June 1996 Dave
Buckingham built a neat p246 glider gun using a century as the
engine. See also bookend and diuresis.

:**chemist** (p5)

:**C-heptomino** Name given by Conway to the following heptomino, a less
common variant of the B-heptomino.

:**Cheshire cat** A block predecessor by C. R. Tompkins that
unaccountably appeared both in Scientific American and in
Winning Ways. See also grin.

:**chicken wire** A type of stable agar of density 1/2. The
simplist version is formed from the tile:

:**cigar** = mango

:**cis-beacon on anvil** (p2)

:**cis-beacon on table** (p2)

:**cis-boat with tail** (p1)

:**cis fuse with two tails** (p1) See also pulsar quadrant.

:**cis-mirrored R-bee** (p1)

:**cis snake** = canoe

:**clean** Opposite of dirty. A reaction which produces a small number
of different products which are desired or which are easily deleted
is said to be clean. For example, a puffer which produces just one
object per period is clean. Clean reactions are useful because they
can be used as building blocks in larger constructions.

When a fuse is said to be clean, or to burn cleanly, this usually means that no debris at all is left behind.

:**clock** (p2) Found by Simon Norton, May 1970. This is the fifth or
sixth most common oscillator, being about as frequent as the
pentadecathlon, but much less frequent than the blinker, toad,
beacon or pulsar. But it's surprisingly rare considering its
small size.

:**clock II** (p4) Compare with pinwheel.

:**cloud of smoke** = smoke

:**cloverleaf** This name was given by Robert Wainwright to his p2
oscillator washing machine. But Achim Flammenkamp also gave this
name to Achim's p4.

:**cluster** Any pattern in which each live cell is connected to every
other live cell by a path that does not pass through two consecutive
dead cells. This sense is due to Nick Gotts, but the term has also
been used in other senses, often imprecise.

:**CNWH** Conweh, creator of the Life universe.

:**Coe ship** (*c*/2 ortogonally, p16) A puffer engine discovered by Tim
Coe in October 1995.

:**Coe's p8** (p8) Found by Tim Coe in August 1997.

:**colorized Life** A cellular automaton which is the same as Life
except for the use of a number of different ON states ("colours").
All ON states behave the same for the purpose of applying the Life
rule, but additional rules are used to specify the colour of the
resulting ON cells. Examples are Immigration and QuadLife.

:**colour of a glider** The colour of a glider is a property of the
glider which remains constant while the glider is moving along a
straight path, but which can be changed when the glider bounces off
a reflector. It is an important consideration when building
something using reflectors.

The colour of a glider can be defined as follows. First
choose some cell to be the origin. This cell is then considered
to be white, and all other cells to be black or white in a
checkerboard pattern. (So the cell with coordinates (*m*,*n*) is
white if *m*+*n* is even, and black otherwise.) Then the colour of
a glider is the colour of its leading cell when it is in a phase
which can be rotated to look like this:

A reflector which does not change the colour of gliders obviously cannot be used to move a glider onto a path of different colour than it started on. But a 90-degree reflector which does change the colour of gliders is similarly limited, as the colour of the resulting glider will depend only on the direction of the glider, no matter how many reflectors are used. For maximum flexibility, therefore, both types of reflector are required.

:**complementary blinker** = fore and back

:**compression** = repeat time

:**conduit** Any arrangement of still lifes and/or oscillators which
move an active object to another location, perhaps also transforming
it into a different active object at the same time, but without
leaving any permanent debris (except perhaps gliders, or other
spaceships) and without any of the still lifes or oscillators being
permanently damaged. Probably the most important conduit is the
following remarkable one (Dave Buckingham, July 1996) in which a
B-heptomino is transformed into a Herschel in 59 generations.

:**confused eaters** (p4) Found by Dave Buckingham before 1973.

:**converter** A conduit in which the input object is not of the same
type as the output object. This term tends to be preferred when
either the input object or the output object is a spaceship.

The following diagram shows a p8 pi-heptomino-to-HWSS converter. This was originally found by Dave Buckingham in a larger form (using a figure-8 instead of the boat). The improvement shown here is by Bill Gosper (August 1996). Dieter Leithner has since found (much larger) oscillators of periods 44, 46 and 60 to replace the Kok's galaxy.

:**convoy** A collection of spaceships all moving in the same direction
at the same speed.

:**Corder-** Prefix used for things involving switch engines, after
Charles Corderman.

:**Corder engine** = switch engine

:**Cordergun** A gun firing Corderships. The first was built by Jason
Summers in July 1999, using a glider synthesis by Stephen Silver.

:**Cordership** Any spaceship based on switch engines. These
necessarily move at a speed of *c*/12 diagonally with a period of 96
(or a multiple thereof). The first was found by Dean Hickerson
in April 1991. Corderships are by far the slowest spaceships yet
constructed, although arbitrarily slow spaceships are known to exist
(see universal constructor). Hickerson's original Cordership used
13 switch engines. He soon reduced this to 10, and in August 1993
to 7. In July 1998 he reduced it to just 6, and this is shown below.

:**cousins** (p3) This contains two copies of the stillater rotor.

:**cover** The following induction coil. See scrubber for an example
of its use.

:**covered table** = cap

:**cow** (*c* p8 fuse)

:**CP pulsar** = pulsar

:**cross** (p3) Found by Robert Wainwright in October 1989.

:**crowd** (p3) Found by Dave Buckingham in January 1973.

:**crown** The p12 part of the following p12 oscillator, where it is
hassled by caterer, a jam and a HW emulator. This oscillator
was found by Noam Elkies in January 1995.

:**crucible** = cauldron

:**crystal** A regular growth that is sometimes formed when a stream of
gliders, or other spaceships, is fired into some junk.

The most common example is initiated by the following collision of a glider with a block. With a glider stream of even period at least 82, this gives a crystal which forms a pair beehives for every 11 gliders which hit it.

:**cuphook** (p3) Found by Rich Schroeppel, October 1970. This is one of
only three essentially different p3 oscillators with only three
cells in the rotor. The others are 1-2-3 and stillater.

:**curl** = loop

:**dart** (*c*/3 ortogonally, p3) Found by David Bell, May 1992.

:**dead spark coil** (p1) Compare spark coil.

:**de Bruijn diagram** = de Bruijn graph

:**de Bruijn graph** As applied to Life, a de Bruijn graph is a
graph showing which pieces can be linked to which other pieces
to form form a valid part of a Life pattern of a particular kind.

For example, if we are interested in still lifes, then we could consider 2×3 rectangular pieces and the de Bruijn graph would show which pairs of these can be overlapped to form 3×3 squares in which the centre cell remains unchanged in the next generation.

David Eppstein's search program gfind is based on de Bruijn graphs.

:**density** The density of a pattern is the limit of the proportion of
live cells in a (2*n*+1)×(2*n*+1) square centred on a particular cell as
*n* tends to infinity, when this limit exists. (Note that it does not
make any difference what cell is chosen as the centre cell. Also
note that if the pattern is finite then the density is zero.) There
are other definitions of density, but this one will do here.

In 1994 Noam Elkies proved that the maximum density of a stable
pattern is 1/2, which had been the conjectured value. See the paper
listed in the bibliography. Marcus Moore provided a simpler proof
in 1995, and in fact proves that a still life with an *m* × *n*
bounding box has at most (*mn*+*m*+*n*)/2 cells.

But what is the maximum average density of an oscillating pattern? The answer is conjectured to be 1/2 again, but this remains unproved. The best upper bound so far obtained is 8/13 (Hartmut Holzwart, September 1992).

The maximum possible density for a phase of an oscillating pattern is also unknown. An example with a density of 3/4 is known (see agar), but densities arbitrarily close to 1 may perhaps be possible.

:**D-heptomino** = Herschel

:**diamond** = tub

:**diamond ring** (p3) Found by Dave Buckingham in 1972.

:**diehard** Any pattern that vanishes, but only after a long time. The
following example vanishes in 130 generations, which is probably the
limit for patterns of 7 or fewer cells. Note that there is no limit
for higher numbers of cells - e.g., for 8 cells we could have a
glider heading towards an arbitrarily distant blinker.

:**dinner table** (p12) Found by Robert Wainwright in 1972.

:**dirty** Opposite of clean. A reaction which produces a large amount
of complicated junk which is difficult to control or use is said
to be dirty. Many basic puffer engines are dirty and need to
be tamed by accompanying spaceships in order to produce clean
output.

:**diuresis** (p90) Found by David Eppstein in October 1998. His original
stabilization used pentadecathlons. The stabilization with
complicated still lifes shown here (in two slightly different
forms) was found by Dean Hickerson the following day. The name is
due to Bill Gosper (see kidney).

:**dock** The following induction coil.

:**domino** The 2-cell polyomino. A number of objects, such as the
HWSS and pentadecathlon, produce domino sparks.

:**do-see-do** The following reaction, found by David Bell in 1996, in
which two gliders appear to circle around each other as they are
reflected 90 degrees by a twin bees shuttle. Four copies of the
reaction can be used to create a p92 glider loop which repeats the
do-see-do reaction forever.

:**double-barrelled** Of a gun, emitting two streams of spaceships
(or rakes). See B-52 bomber for an example.

:**double block reaction** A certain reaction that can be used to
stabilize the twin bees shuttle (qv). This was discovered by
David Bell in October 1996.

The same reaction sometimes works in other situations, as shown in the following diagram where a pair of blocks eats an R-pentomino and a LWSS. (The LWSS version was known at least as early 1994, when Paul Callahan saw it form spontaneously as a result of firing a LWSS stream at some random junk.)

:**double caterer** (p3) Found by Dean Hickerson, October 1989. Compare
caterer and triple caterer.

:**double ewe** (p3) Found by Robert Wainwright before September 1971.

:**double wing** = moose antlers

:**dove** The following induction coil.

:**down boat with tail** = cis-boat with tail

:**dragon** (*c*/6 orthogonally, p6) This spaceship, discovered by
Paul Tooke in April 2000, was the first known *c*/6 spaceship.
All other known *c*/6 spaceships are flotillas involving at
least two dragons.

:**drain trap** = paperclip

:**drifter** A perturbation moving within a stable pattern. Dean
Hickerson has written a program to search for drifters, with the
hope of finding one which could be moved around a track. Because
drifters can be very small, they could be packed more tightly than
Herschels, and so allow the creation of oscillators of periods
not yet attained, and possibly prove that Life is omniperiodic.
Hickerson has found a number of components towards this end, but
it has proved difficult to change the direction of movement of a
drifter, and so far no complete track has been found. However,
Hickerson has had success using the same search program to find
eaters with novel properties, such as that used in diuresis.

:**dual 1-2-3-4** = Achim's p4

:**early universe** Conway's somewhat confusing term for sparse Life.

:**eater** Any still life that has the ability to interact with certain
patterns without suffering any permanent damage. (If it doesn't
suffer even temporary damage then it may be referred to as a rock.)
The eater1 is a very common eater, and the term "eater" is often
used specifically for this object. Other eaters include eater2,
eater3, eater4 and even the humble block. (In fact the block
was the first known eater, being found capable of eating beehives
from a queen bee.) Another useful eater is shown below, feasting
on a glider.

:**eater1** (p1) Usually simply called an eater, and also called a
fishhook. Its ability to eat various objects was discovered by
Bill Gosper in 1971.

:**eater2** (p1) This eater was found by Dave Buckingham in the 1970s.
Mostly it works like the ordinary eater (see eater1) but with two
slight differences that make it useful despite its size: it takes
longer to recover from each bite and it acts like an eater in two
directions. The first property means that, among other things, it
can eat a glider in a position that would destroy a fishhook. This
novel glider-eating action is occasionally of use in itself, and
combined with the symmetry means that an eater2 can eat gliders along
four different paths. An eater2 variant noticed by Stephen Silver in
May 1998 that is useful for obtaining smaller bounding boxes can be
seen under gliderless.

:**eater3** (p1) This large symmetric eater, found by Dave Buckingham,
has a very different eating action from the eater1 and eater2.
The loaf can take bites out things, being flipped over in the
process. The rest of the object merely flips it back again.

:**eater4** (p1) Another eater by Dave Buckingham, which he found in
1971, but did not recognize as an eater until 1975 or 1976. It
can't eat gliders, but it can be used for various other purposes.
The four NE-most centre cells regrow in a few generations after being
destroyed by taking a bite out of something.

:**eater/block frob** (p4) Found by Dave Buckingham in 1976 or earlier.

:**eater-bound pond** = biting off more than they can chew

:**eater-bound Z-hexomino** = pentoad

:**eater eating eater** = two eaters

:**eater plug** (p2) Found by Robert Wainwright, February 1973.

:**eaters +** = French kiss

:**eaters plus** = French kiss

:**ecologist** (*c*/2 orthogonally, p20) This consists of the classic
puffer train with a LWSS added to suppress the debris. See
also space rake.

:**edge-repair spaceship** A spaceship which has an edge that possesses
no spark and yet is able to perturb things because of its
ability to repair certain types of damage to itself. The most
useful examples are the following two small p3 *c*/3 spaceships:

:**edge shooter** A gun which fires its gliders (or whatever) right
at the edge of the pattern, so that it can be used to fire them
closely parallel to others. This is useful for constructing
complex guns. Compare glider pusher, which can in fact be used
for making edge shooters.

The following diagram shows a p46 edge shooter found by Paul Callahan in June 1994.

:**edge spark** A spark at the side of a spaceship that can be
used to perturb things as the spaceship passes by.

:**edge sparker** A spaceship that produces one or more edge sparks.

:**egg** = non-spark

:**E-heptomino** Name given by Conway to the following heptomino.

:**elbow ladder** Scot Ellison's name for the type of pattern he
created in which one or more gliders shuttle back and forth (using
the kickback reaction) deleting the output gliders from a pair of
slide guns.

:**electric fence** (p5) A stabilization of ants. Dean Hickerson,
February 1993.

:**elevener** (p1)

:**Elkies' p5** (p5) Found by Noam Elkies in 1997.

:**emu** Dave Buckingham's term for a Herschel loop that does not emit
gliders (and so is "flightless"). All known Herschel loops of
periods 57, 58, 59 and 61 are emus. See also Quetzal.

:**emulator** Any one of three p4 oscillators that produce sparks
similar to those produced by LWSS, MWSS and HWSS. See
LW emulator, MW emulator and HW emulator. Larger emulators
are also possible, but they require stabilizing objects to suppress
their non-sparks and so are of little use. The emulators were
discovered by Robert Wainwright in June 1980.

:**engine** The active portion of an object (usually a puffer or gun)
which is considered to actually produce its output, and which
generally permits no variation in how it works. The other parts of
the object are just there to support the engine. For examples, see
puffer train, Schick engine, blinker puffer, frothing puffer
and line puffer.

:**en retard** (p3) Found by Dave Buckingham, August 1972.

:**Enterprise** (*c*/4 diagonally, p4) Found by Dean Hickerson, March 1993.

:**Eureka** (p30) A pre-pulsar shuttle found by Dave Buckingham in
August 1980. A variant is obtained by shifting the top half two
spaces to either side.

:**evolutionary factor** For an unstable pattern, the time to
stabilization divided by the initial population. For example,
the R-pentomino has an evolutionary factor of 220.6, while
bunnies has an evolutionary factor of 1925.777... The term
is no longer in use.

:**exposure** = underpopulation

:**extra extra long** = long^4

:**extra long** = long^3

:**extremely impressive** (p6) Found by Dave Buckingham, August 1976.

:**factory** Another word for gun, but not used in the case of glider
guns. The term is also used for a pattern that repeatedly
manufactures objects other than spaceships or rakes. In this
case the new objects do not move out of the way, and therefore must
be used up in some way before the next one is made. The following
shows an example of a p144 gun which consists of a p144 block
factory whose output is converted into gliders by a p72 oscillator.
(This gun is David Bell's improvement of the one Bill Gosper found
in July 1994. The p72 oscillator is by Robert Wainwright, 1990, and
the block factory is Achim's p144 minus one of its stabilizing
blocks.)

:**familiar fours** Common patterns of four identical objects. The
five commonest are traffic light (4 blinkers), honey farm
(4 beehives), blockade (4 blocks), fleet (4 ships, although
really 2 ship-ties) and bakery (4 loaves, although really 2
bi-loaves).

:**fanout** A mechanism that emits two or more objects of some type for
each one that it receives. Typically the objects are gliders or
Herschels; glider duplicators are a special case.

:**Fast Forward Force Field** The following reaction found by Dieter
Leithner in May 1994. In the absence of the incoming LWSS the
gliders would simply annihilate one another, but as shown they
allow the LWSS to advance 11 spaces in the course of the next 6
generations. A neat illusion. See also star gate. (Leithner
named the Fast Forward Force Field in honour of his favourite
science fiction writer, the physicist Robert L. Forward.)

:**father** = parent

:**featherweight spaceship** = glider

:**fencepost** Any pattern that stabilizes one end of a wick.

:**Fermat prime calculator** A pattern constructed by Jason Summers in
January 2000 that exhibits infinite growth if and only if there
are no Fermat primes greater than 65537. The question of whether
or not it really does exhibit infinite growth is therefore equivalent
to a well-known and long-standing unsolved mathematical problem.
It will, however, still be growing at generation 10^{2585827975}.
The pattern is based on Dean Hickerson's primer and caber tosser
patterns and a p8 beehive puffer by Hartmut Holzwart.

:**F-heptomino** Name given by Conway to the following heptomino.

:**figure-8** (p8) Found by Simon Norton in 1970.

:**filter** Any oscillator used to delete some but not all of the
spaceships in a stream. An example is the blocker, which can
be positioned so as to delete every other glider in a stream of
period 8*n*+4, and can also do the same for LWSS streams. Other
examples are the MW emulator and T-nosed p4 (either of which
can be used to delete every other LWSS in a stream of period 4*n*+2),
the fountain (which does the same for MWSS streams) and a number
of others, such as the p6 pipsquirter, the pentadecathlon and
the p72 oscillator shown under factory. Another example, a p4
oscillator deleting every other HWSS in a stream of period 4*n*+2, is
shown below. (The p4 oscillator here was found, with a slightly
larger stator, by Dean Hickerson in November 1994.)

:**fish** A generic term for LWSS, MWSS and HWSS, or, more
generally, for any spaceship.

:**fishhook** = eater1

:**fleet** (p1) A common formation of two ship-ties.

:**flip-flop** Any p2 oscillator. However, the term is also used
in two more specific (and non-equivalent) senses: (a) any p2
oscillator whose two phases are mirror images of one another,
and (b) any p2 oscillator in which all rotor cells die from
underpopulation. In the latter sense it contrasts with on-off.
The term has also been used even more specifically for the 12-cell
flip-flop shown under phoenix.

:**flip-flops** Another name for the flip-flop shown under phoenix.

:**flipper** Any oscillator or spaceship that forms its mirror image
halfway through its period.

:**flotilla** A spaceship composed of a number of smaller interacting
spaceships. Often one or more of these is not a true spaceship and
could not survive without the support of the others. The following
example shows an OWSS escorted by two HWSS.

:**fly** A certain *c*/3 tagalong found by David Bell, April 1992.
Shown here attached to the back of a small spaceship (also by Bell).

:**flying machine** = Schick engine

:**fore and back** (p2) Compare snake pit. Found by Achim Flammenkamp,
July 1994.

:**forward glider** A glider which moves at least partly in the same
direction as the puffer(s) or spaceship(s) under consideration.

:**fountain** (p4) Found by Dean Hickerson in November 1994, and named by
Bill Gosper. See also filter.

:**fourteener** (p1)

:**fox** (p2) This is the smallest asymmetric p2 oscillator. Found by
Dave Buckingham, July 1977.

:**French kiss** (p3) Found by Robert Wainwright, July 1971.

:**frog II** (p3) Found by Dave Buckingham, October 1972.

:**frothing puffer** A frothing puffer (or a frothing spaceship) is a
puffer (or spaceship) whose back end appears to be unstable and
breaking apart, but which nonetheless survives. The exhaust festers
and clings to the back of the puffer/spaceship before breaking off.
The first known frothing puffers were *c*/2, and most were found by
slightly modifying the back ends of p2 spaceships. A number of
these have periods which are not a multiple of 4 (as with some
line puffers). Paul Tooke has also found *c*/3 frothing puffers.

The following p78 *c*/2 frothing puffer was found by Paul Tooke in
April 2001.

:**frothing spaceship** See frothing puffer.

:**fumarole** (p5) Found by Dean Hickerson in September 1989. In terms of
its 7×8 bounding box this is the smallest p5 oscillator.

:**fuse** A wick burning at one end. For examples, see baker,
beacon maker, blinker ship, boat maker, cow, harvester,
lightspeed wire, pi ship, reverse fuse, superstring and
washerwoman. Useful fuses are usually clean.

:**Gabriel's p138** (p138) The following oscillator found by Gabriel
Nivasch in October 2002.

:**galaxy** = Kok's galaxy

:**Game of Life** = Life

:**Garden of Eden** A configuration of ON and OFF cells that can only
occur in generation 0. (This term was first used in connection with
cellular automata by John W. Tukey, many years before Life.) It was
known from the start that there are Gardens of Eden in Life, because
of a theorem by Edward Moore that guarantees their existence in
a wide class of cellular automata. Explicit examples have since
been constructed, the first by Roger Banks, et al. at MIT in 1971.
This example was 9 × 33. In 1974 J. Hardouin-Duparc, et al. produced
a 6 × 122 example. The following shows a 14 × 14 example (with 143
ON cells) by Achim Flammenkamp (1991 or 1992).

:**generation** The fundamental unit of time. The starting pattern is
generation 0.

:**germ** (p3) Found by Dave Buckingham, September 1972.

:**gfind** A program by David Eppstein which uses de Bruijn graphs to
search for new spaceships. It was with gfind that Eppstein found
the weekender, and Paul Tooke later used it to find the dragon.
It is available at http://www.ics.uci.edu/~eppstein/ca/gfind.c
(C source code only).

Compare lifesrc.

:**GIG** A glider injection gate. This is a device for injecting a
glider into a glider stream. The injected glider is synthesized
from one or more incoming spaceships assisted by the presence of
the GIG. (This contrasts with some other glider injection reactions
which do not require a GIG.) Gliders already in the glider stream
pass through the GIG without interfering with it. A GIG usually
consists of a small number of oscillators.

Glider injection gates are useful for building glider guns with
pseudo-periods that are of the form *nd*, where *n* is a positive
integer, and *d* is a proper divisor of some convenient base gun period
(such as 30 or 46), with *d* > 13.

:**glasses** (p2) Compare scrubber and spark coil.

:**glider** (*c*/4 diagonally, p4) The smallest, most common and first
discovered spaceship. This was found by Richard Guy in 1970
while Conway's group was attempting to track the evolution of the
R-pentomino. The name is due in part to the fact that it is
glide symmetric. (It is often stated that Conway discovered the
glider, but he himself has said it was Guy. See also the cryptic
reference ("some guy") in Winning Ways.)

:**glider-block cycle** An infinite oscillator based on the following
reaction (a variant of the rephaser). The oscillator consists of
copies of this reaction displaced 2*n* spaces from one another (for
some *n*>6) with blocks added between the copies in order to cause the
reaction to occur again halfway through the period. The period of
the resulting infinite oscillator is 8*n*-20. (Alternatively, in a
cylindrical universe of width 2*n* the oscillator just consists of two
gliders and two blocks.)

:**glider construction** = glider synthesis

:**glider duplicator** Any reaction in which one input glider is
converted into two output gliders. This can be done either
by oscillators or by spaceships. The most useful glider
duplicators are those with low periods.

The following period 30 glider duplicator demonstrates a simple glider duplicating mechanism found by Dieter Leithner. The input glider stream comes in from the upper left, and the output glider streams leave at the upper and lower right. One of the output glider streams is inverted, so an inline inverter is required to complete the duplicator.

Spaceship convoys which can duplicate gliders are very useful since they (along with glider turners) provide a means to clean up many dirty puffers by duplicating and turning output gliders so as to impact into the exhaust to clean it up.

Glider duplicators (and turners) are known for backward gliders
using p2 *c*/2 spaceships, and for forward gliders using p3 *c*/3
spaceships. These are the most general duplicators for these speeds.

:**glider gun** A gun which fires gliders.

:**glider injection gate** = GIG

:**gliderless** A gun is said to be gliderless if it does not use
gliders. The purist definition would insist that a glider does
not appear anywhere, even incidentally. For a long time the only
known way to construct LWSS, MWSS and HWSS guns involved
gliders, and it was not until April 1996 that Dieter Leithner
constructed the first gliderless gun (a p46 LWSS gun). The following
diagram shows Leithner's p44 MWSS gun which he discovered in April
1997 (shown with Stephen Silver's May 1998 improvement to the
bounding box using a modified eater2). This is the smallest
known gliderless gun, and also the smallest known MWSS gun. It is
based on an important p44 oscillator discovered by Dave Buckingham
in early 1992. (Note that a glider shape appears in this gun for
three consecutive generations, but always as part of a larger
cluster, so even a purist would regard this gun as gliderless.)

:**glider pusher** An arrangement of a queen bee shuttle and a
pentadecathlon that can push the path of a passing glider
out by one half-diagonal space. This was found by Dieter Leithner
in December 1993 and is shown below. It is useful for constructing
complex guns where it may be necessary to produce a number of
gliders travelling on close parallel paths. See also edge shooter.

:**gliders by the dozen** (stabilizes at time 184) In early references
this is usually shown in a larger form whose generation 1 is
generation 8 of the form shown here.

:**glider synthesis** Construction of an object by means of glider
collisions. It is generally assumed that the gliders should be
arranged so that they could come from infinity - that is, gliders
should not have had to pass through one another to achieve the
initial arrangement.

Glider syntheses for all still lifes and known oscillators with at most 14 cells were found by Dave Buckingham.

Perhaps the most interesting glider syntheses are those of
spaceships, because these can be used to create corresponding
guns and rakes. Many of the *c*/2 spaceships that are based on
standard spaceships have been synthesized, mostly by Mark Niemiec.
In June 1998 Stephen Silver found syntheses for some of the
Corderships (although it was not until July 1999 that Jason Summers
used this to build a Cordership gun). In May 2000, Noam Elkies
suggested that a 2*c*/5 spaceship found by Tim Coe in May 1996 might be
a candidate for glider synthesis. Initial attempts to construct a
synthesis for this spaceship got fairly close, but it was only in
March 2003 that Summers and Elkies managed to find a way perform the
crucial last step. Summers then used the new synthesis to build a
*c*/2 forward rake for the 2*c*/5 spaceship; this was the first example
in Life of a rake which fires spaceships that travel in the same
direction as the rake but more slowly.

A 3-glider synthesis of a pentadecathlon is shown in the diagram below. This was found in April 1997 by Heinrich Koenig and came as a surprise, as it was widely assumed that anything using just three gliders would already be known.

:**glider train** A certain puffer that produces two rows of blocks
and two backward glider waves. Ten of these were used to make the
first breeder.

:**glider turner** An reaction in which a glider is turned by an
oscillator or a spaceship. In the former case, the glider
turner is usually called a reflector.

Glider turners are easily built using standard spaceships. The following diagram shows a convoy which turns a forward glider 90 degrees, with the new glider also moving forwards.

Small rearrangements of the back two spaceships can alternatively send the output glider into any of the other three directions.See also glider duplicator and reflector.

:**glide symmetric** Undergoing simultaneous reflection and translation.
A glide symmetric spaceship is commonly called a flipper.

:**gnome** = fox

:**GoE** = Garden of Eden

:**GoL** = Game of Life

:**Gosper glider gun** The first known gun, and indeed the first
known finite pattern with unbounded growth, found by Bill Gosper
in November 1970. It remains by far the smallest known gun.
Gosper has since found other guns, see new gun and the p144
gun shown under factory.

:**gourmet** (p32) Found by Dave Buckingham in March 1978. Compare with
pi portraitor and popover.

:**grammar** A set of rules for connecting components together to make
an object such as a spaceship, oscillator or still life.

:**grandfather** = grandparent

:**grandparent** A pattern is said to be a grandparent of the pattern it
gives rise to after two generations. See also parent.

:**Gray counter** (p4) Found in 1971. If you look at this in the right
way you will see that it cycles through the Gray codes from 0 to 3.
Compare with R2D2.

:**great on-off** (p2)

:**grey counter** = Gray counter (This form is erroneous, as Gray is
surname, not a colour.)

:**grin** The following common parent of the block. This name relates
to the infamous Cheshire cat. See also pre-block.

:**growing spaceship** An object that moves like a spaceship, except
that its front part moves faster than its back part and a wick
extends between the two. Put another way, a growing spaceship is
a puffer whose output is burning cleanly at a slower rate than
the puffer is producing it. Examples include blinker ships and
pi ships.

:**gull** = elevener

:**gun** Any stationary pattern that emits spaceships (or rakes)
forever. For examples see double-barrelled, edge shooter,
factory, gliderless, Gosper glider gun, new gun and true.

:**gunstar** Any of a series of glider guns of period 144+72*n* (for all
non-negative integers *n*) constructed by Dave Buckingham in 1990
based on his transparent block reaction and Robert Wainwright's
p72 oscillator (shown under factory).

:**half bakery** See bi-loaf.

:**half fleet** = ship-tie

:**hammer** To hammer a LWSS, MWSS or HWSS is to smash things into
the rear end of it in order to transform it into a different type
of spaceship. A hammer is the object used to do the hammering.
In the following example by Dieter Leithner a LWSS is hammered by
two more LWSS to make it into a MWSS.

:**hammerhead** A certain front end for *c*/2 spaceships. The central
part of the hammerhead pattern is supported between two MWSS.
The picture below shows a small example of a spaceship with a
hammerhead front end (the front 9 columns).

:**handshake** An old MIT name for lumps of muck, from the following
form (2 generations on from the stairstep hexomino):

:**harbor** (p5) Found by Dave Buckingham in September 1978. The name is
by Dean Hickerson.

:**harvester** (*c* p4 fuse) Found by David Poyner, this was the first
published example of a fuse. The name refers to the fact the
it produces debris in the form of blocks which contain the same
number of cells as the fuse has burnt up.

:**hashlife** A Life algorithm by Bill Gosper that is designed to take
advantage of the considerable amount of repetitive behaviour in many
large patterns of interest. This algorithm is described by Gosper
in his paper listed in the bibliography at the end of this lexicon.
Roughly speaking, the idea is to store subpatterns in a hash table so
that the results of their evolution don't have to be recomputed if
they arise again somewhen, or somewhere, else. This does, however,
mean that complex patterns can require substantial amounts of memory.
Hashlife provides a means of evolving repetitive patterns millions
(or even billions or trillions) of generations further than normal
Life algorithms can manage in a reasonable amount of time. It is
not, however, suitable for showing a continuous display of the
evolution of a pattern, because it works asynchronously - at any
given moment it will usually have evolved different parts of the
pattern through different numbers of generations.

:**hassler** An oscillator that works by hassling (repeatedly moving
or changing) some object. For some examples, see Jolson,
baker's dozen, toad-flipper, toad-sucker and traffic circle.

:**hat** (p1) Found in 1971. See also twinhat and sesquihat.

:**heat** For an oscillator or spaceship, the average number of cells
which change state in each generation. For example, the heat of a
glider is 4, because 2 cells are born and 2 die every generation.

For a period *n* oscillator with an *r*-cell rotor the heat is at
least 2*r*/*n* and no more than *r*(1-(*n* mod 2)/*n*). For *n*=2 and *n*=3 these
bounds are equal.

:**heavyweight emulator** = HW emulator

:**heavyweight spaceship** = HWSS

:**heavyweight volcano** = HW volcano

:**hebdarole** (p7) Found by Noam Elkies, November 1997. Compare
fumarole. The smaller version shown below was found soon after by
Alan Hensel using a component found by Dave Buckingham in June 1977.
The top tens rows can be stabilized by their mirror image (giving
an inductor) and this was the original form found by Elkies.

:**hectic** (p30) Found by Robert Wainwright in September 1984.

:**Heisenburp device** A pattern which can detect the passage of a
glider without affecting the glider's path or timing. The first
such device was constructed by David Bell in December 1992. The
term is due to Bill Gosper.

The following is an example of the kind of reaction used at the heart of a Heisenburp device. The glider at bottom right alters the reaction of the other two gliders without itself being affected in any way.

:**heptaplet** Any 7-cell polyplet.

:**heptapole** (p2) The barberpole of length 7.

:**heptomino** Any 7-cell polyomino. There are 108 such objects.
Those with names in common use are the B-heptomino, the
Herschel and the pi-heptomino.

:**Herschel** (stabilizes at time 128) The following pattern which
occurs at generation 20 of the B-heptomino.

:**Herschel conduit** A conduit that moves a Herschel from one place
to another. See also Herschel loop.

Sixteen simple stable Herschel conduits are currently known, having been discovered from 1995 onwards by Dave Buckingham (DJB) and Paul Callahan (PBC). (Of course, the number depends on what is meant by "simple".) These are shown in the following table. In this table "steps" is the number of steps, "m" tells how the Herschel is moved (R = turned right, L = turned left, B = turned back, F = unturned, f = flipped), and "dx" and "dy" give the displacement of the centre cell of the Herschel (assumed to start in the orientation shown above).

------------------------------------ steps m dx dy discovery ------------------------------------ 64 R -11 9 DJB, Sep 1995 77 Ff -25 -8 DJB, Aug 1996 112 L -12 -33 DJB, Jul 1996 116 F -32 1 PBC, Feb 1997 117 F -40 -6 DJB, Jul 1996 119 Ff -20 14 DJB, Sep 1996 125 Bf 9 -17 PBC, Nov 1998 153 Ff -48 -4 PBC, Feb 1997 156 L -17 -41 DJB, Aug 1996 158 Ff -27 -5 DJB, Jul 1996 166 F -49 3 PBC, May 1997 176 Ff -45 0 PBC, Oct 1997 190 R -24 16 DJB, Jul 1996 200 Lf -17 -40 PBC, Jun 1997 202 Rf -7 32 DJB, May 1997 222 Bf 6 -16 PBC, Oct 1998 ------------------------------------

See also Herschel transceiver.

:**Herschel loop** A cyclic Herschel track. Although no loop of length
less than 256 generations has been constructed it is possible to make
oscillators of smaller periods by putting more than one Herschel in
the track. In this way oscillators, and in most cases guns, of all
periods from 54 onwards can now be constructed (although the p55 case
is a bit strange, shooting itself with gliders in order to stabilize
itself). See also emu and omniperiodic.

:**Herschel receiver** A pattern found by Paul Callahan in 1996, as
part of the first stable glider reflector. Used as a receiver,
it converts two parallel input gliders (with path separations of
2, 5, or 6) to an R-pentomino, which is then converted to a
Herschel by one of two known mechanisms (the first of which was
found by Dave Buckingham way back in 1972, and the second by
Stephen Silver in October 1997). The version using Buckingham's
R-to-Herschel converter is shown below.

:**Herschel track** A track for Herschels. See also B track.

:**Herschel transceiver** An adjustable Herschel conduit made up of a
Herschel transmitter and a Herschel receiver. The intermediate
stage consists of two gliders on parallel tracks, so the
transmitter and receiver can be separated by any required distance.
The conduit may be stable, or may contain low-period oscillators.

:**Herschel transmitter** Any Herschel-to-glider converter that
produces two gliders on parallel tracks which can be used as input
to a Herschel receiver. If the gliders are far enough apart, a
suitably oriented mirror image of the receiver will also work: the
first glider triggers the receiver and the second glider deletes the
extra beehive.

The following diagram shows a stable Herschel transmitter found by Paul Callahan in May 1997:

Examples of small reversible p6 and p7 transmitters are also known.:**Hertz oscillator** (p8) Compare negentropy, and also cauldron.
Found by Conway's group in 1970.

:**hexadecimal** = beehive and dock

:**hexaplet** Any 6-cell polyplet.

:**hexapole** (p2) The barberpole of length 6.

:**hexomino** Any 6-cell polyomino. There are 35 such objects.
For some examples see century, stairstep hexomino, table,
toad and Z-hexomino.

:**H-heptomino** Name given by Conway to the following heptomino. After
one generation this is the same as the I-heptomino.

:**hive** = beehive

:**hivenudger** (*c*/2 orthogonally, p4) A spaceship found by Hartmut
Holzwart in July 1992. (The name is due to Bill Gosper.) It
consists of a pre-beehive escorted by four LWSS. In fact any
LWSS can be replaced by a MWSS or a HWSS, so that there are 45
different single-hive hivenudgers.

:**honeycomb** (p1)

:**honey farm** (p1) A common formation of four beehives.

:**hook** Another term for a bookend. It is also used for other
hook-shaped things, such as occur in the eater1 and the
hook with tail, for example.

:**hook with tail** (p1) For a long time this was the smallest
still life without a well-established name. It is now a vital
component of the smallest known HWSS gun, where it acts as a
rock.

:**houndstooth agar** The p2 agar that results from tiling the plane
with the following pattern.

:**house** The following induction coil. It is generation 3 of the
pi-heptomino. See spark coil and dead spark coil.

:**hustler** (p3) Found by Robert Wainwright, June 1971.

:**hustler II** (p4)

:**HW emulator** (p4) Found by Robert Wainwright in June 1980. See also
emulator.

:**HWSS** (*c*/2 orthogonally, p4) The fourth most common spaceship.
Found by Conway in 1970.

:**HWSS emulator** = HW emulator

:**HW volcano** (p5) A p5 domino sparker, found by Dean Hickerson in
February 1995. There are at least two known forms for this, one of
which is shown below.

:**I-heptomino** Name given by Conway to the following heptomino. After
one generation this is the same as the H-heptomino.

:**IMG** = intermitting glider gun

:**Immigration** A form of colorized Life in which there are two types
of ON cell, a newly-born cell taking the type of the majority of its
three parent cells and surviving cells remaining of the same type
as in the previous generation.

:**induction coil** Any object used to stabilize an edge (or edges)
without touching. The tubs used in the Gray counter are examples,
as are the blocks and snakes used in the Hertz oscillator and the
heptomino at the bottom of the mathematician.

:**inductor** Any oscillator with a row of dead cells down the middle
and whose two halves are mirror images of one another, both halves
being required for the oscillator to work. The classic examples are
the pulsar and the tumbler. If still lifes are considered as
p1 oscillators then there are numerous simple examples such as
table on table, dead spark coil and cis-mirrored R-bee.
Some spaceships, such as the brain, the snail and the spider
use the same principle.

:**infinite glider hotel** A pattern by David Bell, named after Hilbert's
"infinite hotel" scenario in which a hotel with an infinite number of
rooms has room for more guests even if it is already full, simply by
shuffling the old guests around.

In this pattern, two pairs of Corderships moving at *c*/12 are
pulling apart such that there is an ever-lengthening glider track
between them. Every 128 generations another glider is injected into
the glider track, joining the gliders already circulating there.
The number of gliders in the track therefore increases without limit.

The tricky part of this construction is that even though all the previously injected gliders are repeatedly flying through the injection point, that point is guaranteed to be empty when it is time for the next glider to be injected.

:**infinite growth** Growth of a finite pattern such that the
population tends to infinity, or at least is unbounded.
The first known pattern with infinite growth was the
Gosper glider gun.

An interesting question is: What is the minimum population of a pattern that exhibits infinite growth? In 1971 Charles Corderman found that a switch engine could be stabilized by a pre-block in a number of different ways, giving 11-cell patterns with infinite growth. This record stood for more than quarter of a century until Paul Callahan found, in November 1997, two 10-cell patterns with infinite growth. The following month he found the one shown below, which is much neater, being a single cluster. This produces a stabilized switch engine of the block-laying type.

Nick Gotts and Paul Callahan have also shown that there is no infinite growth pattern with fewer than 10 cells, so that the question has now been answered.Also of interest is the following pattern (again found by Callahan), which is the only 5×5 pattern with infinite growth. This too emits a block-laying switch engine.

Following a conjecture of Nick Gotts, Stephen Silver produced, in May 1998, a pattern of width 1 which exhibits infinite growth. This pattern was very large (12470×1 in the first version, reduced to 5447×1 the following day). In October 1998 Paul Callahan did an exhaustive search, finding the smallest example, the 39×1 pattern shown below. This produces two block-laying switch engines, stability being achieved at generation 1483.

Although the simplest infinite growth patterns grow at a rate that is (asymptotically) linear, many other types of growth rate are possible, quadratic growth (see breeder) being the fastest. Dean Hickerson has found many patterns with unusual growth rates, such as sawtooths and a caber tosser.

See also Fermat prime calculator.

:**initials** = monogram

:**inline inverter** The following reaction in which a p30 gun can be
used to invert the presence or absence of gliders in a p30 stream,
with the output glider stream being in the same direction as the
input glider stream.

:**integral** = integral sign

:**integral sign** (p1)

:**intentionless** = elevener

:**interchange** (p2) A common formation of six blinkers.

:**intermitting glider gun** Despite the name, an intermitting glider gun
(IMG) is more often an oscillator than a gun. There are two
basic types. A type 1 IMG consists of two guns firing at one another
in such a way that each gun is temporarily disabled on being hit
by a glider from the other gun. A type 2 IMG consists of a single
gun firing at a 180-degree glider reflector in such a way that
returning gliders temporarily disable the gun.

Both types of IMG can be used to make glider guns of periods that are multiples of the base period. This is done by firing another gun across the two-way intermittent glider stream of the IMG in such a way that gliders only occasionally escape.

:**island** The individual polyplets of which a stable pattern
consists are sometimes called islands. So, for example, a boat
has only one island, while an aircraft carrier has two, a
honey farm has four and the standard form of the eater3 has five.

:**J** = Herschel

:**jack** (p4) Found by Robert Wainwright, April 1984.

:**jam** (p3) Found by Achim Flammenkamp in 1988, but not widely known
about until its independent discovery (and naming) by Dean Hickerson
in September 1989. Compare with mold. In fact this is really very
like caterer. In terms of its 7×7 bounding box it ties with
trice tongs as the smallest p3 oscillator.

:**Jaws** A breeder constructed by Nick Gotts in February 1997. In the
original version Jaws had an initial population of 150, which at
the time was the smallest for any known pattern with superlinear
growth. In November 1997 Gotts produced a 130-cell Jaws using
some switch engine predecessors found by Paul Callahan. Jaws
has since been beaten by the even smaller mosquitos, teeth,
catacryst and metacatacryst.

Jaws consists of eight pairs of switch engines which produce a new block-laying switch engine (plus masses of junk) every 10752 generations. It is therefore an MMS breeder.

:**JC** = dead spark coil

:**JHC** John Horton Conway. Also another name for monogram.

:**J-heptomino** = Herschel

:**Jolson** (p15) Two blocks hassled by two pentadecathlons.
Found by Robert Wainwright in November 1984 and named by Bill
Gosper. A p9 version using snackers instead of pentadecathlons
is also possible.

:**keys** See short keys, bent keys and odd keys.

:**kickback reaction** The following collision of two gliders whose
product is a single glider travelling in the opposite direction
to one of the original gliders. This is important in the proof
of the existence of a universal constructor, and in Bill Gosper's
total aperiodic, as well as a number of other constructions.

:**kidney** A Gosperism for century. See also diuresis.

:**killer toads** A pair of toads acting together so that they can eat
things. Here, for example, are some killer toads eating a HWSS.
Similarly they can eat a MWSS (but not a LWSS). For another
example see twirling T-tetsons II. See also candlefrobra.

:**Klein bottle** As an alternative to a torus, it's possible to make
a finite Life universe in the form of a Klein bottle. The simplest
way to do this is to use an *m* × *n* rectangle with the top edge joined
to the bottom edge (as for a torus) and the left edge twisted and
joined to the right.

:**knightship** Any spaceship of type (2*m*,*m*)/*n*. Such spaceships do
exist (see universal constructor), but no concrete example is
known. A knightship must be asymmetric and its period must be at
least 6, which makes searching for them using programs like lifesrc
very difficult.

By analogy with the corresponding fairy chess pieces, spaceships of
types (3*m*,*m*)/*n*, (3*m*,2*m*)/*n* and (4*m*,*m*)/*n* would presumably be called
camelships, zebraships and giraffeships, respectively. But no
examples of these are known either, and they are even more difficult
to search for.

:**Kok's galaxy** (p8) Found by Jan Kok in 1971. See converter for a
use of this sparker.

:**lake** Any still life consisting of a simple closed curve made from
diagonally connected dominoes. The smallest example is the
pond, and the next smallest is this (to which the term is
sometimes restricted):

:**Laputa** (p2) Found by Rich Schroeppel, September 1992.

:**large S** = big S

:**Life** A 2-dimensional 2-state cellular automaton discovered by
John Conway in 1970. The states are referred to as ON and OFF (or
live and dead). The transistion rule is as follows: a cell that is
ON will remain ON in the next generation if and only if exactly 2
or 3 of the 8 adjacent cells are also ON, and a cell that is OFF will
turn ON if and only if exactly 3 of the 8 adjacent cells are ON.
(This is more succinctly stated as: "If 2 of your 8 nearest
neighbours are ON, don't change. If 3 are ON, turn ON. Otherwise,
turn OFF.")

:**Life32** A freeware Life program by Johan Bontes for Microsoft Windows
95/98/ME/NT/2000/XP.

:**LifeLab** A shareware Life program by Andrew Trevorrow for the
Macintosh (MacOS 8.6 or later).

:**LifeLine** A newletter edited by Robert Wainwright from 1971 to 1973.
During this period it was the main forum for discussions about Life.
The newletter was nominally quarterly, but the actual dates of its
eleven issues were as follows:

Mar, Jun, Sep, Dec 1971 Sep, Oct, Nov, Dec 1972 Mar, Jun, Sep 1973

:**Lifenthusiast** A Life enthusiast. Term coined by Robert Wainwright.

:**lifesrc** David Bell's Life search program, for finding new
spaceships and oscillators. This is a C implementation of an
algorithm developed by Dean Hickerson in 6502 assembler. Most of
the spaceships and many of the oscillators shown in this lexicon
were found with lifesrc or by Hickerson's original program.

Although lifesrc itself is a command-line program, Jason Summers has made a GUI version called WinLifeSearch for Microsoft Windows.

The lifesrc algorithm is only useful for very small periods, as the amount of computing power required rises rapidly with increasing period. For most purposes, period 7 is the practical limit with current hardware.

Lifesrc is available from http://www.canb.auug.org.au/~dbell/ (source code only).

Compare gfind.

:**light bulb** (p2) Found in 1971.

:**lightspeed ribbon** = superstring

:**lightspeed wire** Any wick that can burn non-destructively at the
speed of light. These are potentially useful for various things,
but so far no one has found the necessary mechanisms. The
following diagram shows an example of a lightspeed wire, with a
small defect that travels along it at the speed of light.

:**lightweight emulator** = LW emulator

:**lightweight spaceship** = LWSS

:**lightweight volcano** = toaster

:**line puffer** A puffer which produces its output by means of an
orthogonal line of cells at right angles to the direction of travel.
The archetypal line puffer was found by Alan Hensel in March 1994,
based on a spaceship found earlier that month by Hartmut Holzwart.
The following month Holzwart found a way to make extensible *c*/2 line
puffers, and Hensel found a much smaller stabilization the following
day. But in October 1995 Tim Coe discovered that for large widths
these were often unstable, although typically lasting millions of
generations. In May 1996, however, Coe found a way to fix the
instability. The resulting puffers appear to be completely stable
and to exhibit an exponential increase in period as a function of
width, although neither of these things has been proved.

Line puffers have enabled the construction of various difficult
periods for *c*/2 spaceships and puffers, including occasionally
periods which are not multiples of 4 and which would therefore be
impossible to attain with the usual type of construction based on
standard spaceships. (See frothing puffer for another method
of constructing such periods.) In particular, the first *c*/2 rake
with period not divisible by 4 was achieved in January 2000 when
David Bell constructed a p42 backrake by means of line puffers.

See also puff suppressor.

:**loading dock** (p3) Found by Dave Buckingham, September 1972.

:**loaf** (p1)

:**loaflipflop** (p15) Here four pentadecathlons hassle a loaf.
Found by Robert Wainwright in 1990.

:**loaf on loaf** = bi-loaf

:**loaf siamese barge** (p1)

:**LoM** = lumps of muck

:**lone dot agar** An agar in which every live cell is isolated in every
generation.

:**lonely bee** = worker bee

:**long** A term applied to an object that is of the same basic form
as some standard object, but longer. For examples see long barge,
long boat, long bookend, long canoe, long shillelagh,
long ship and long snake.

:**long^3** The next degree of longness after long long. Some people
prefer "extra long".

:**long^4** The next degree of longness after long^3. Some people
prefer "extra extra long".

:**long barge** (p1)

:**long boat** (p1)

:**long bookend** The following induction coil, longer than a bookend.

:**long canoe** (p1)

:**long hat** = loop

:**long hook** = long bookend

:**long house** = dock

:**long integral** (p1)

:**long long** The next degree of longness after long. Some people
prefer "very long".

:**long long barge** (p1)

:**long long boat** (p1)

:**long long canoe** (p1)

:**long long ship** (p1)

:**long long snake** (p1)

:**long shillelagh** (p1)

:**long ship** (p1)

:**long sinking ship** = long canoe

:**long snake** (p1)

:**loop** (p1)

:**low-denisty Life** = sparse Life

:**lumps of muck** The common evolutionary sequence that ends in the
blockade. The name is sometimes used of the blockade itself,
and can in general be used of any stage of the evolution of the
stairstep hexomino.

:**LW emulator** (p4) The smallest (and least useful) emulator, found by
Robert Wainwright in June 1980.

:**LWSS** (*c*/2 orthogonally, p4) The smallest known orthogonally
moving spaceship, and the second most common (after the
glider). Found by Conway in 1970.

:**LWSS emulator** = LW emulator

:**LWTDS** Life Worker Time Deficiency Syndrome. Term coined by Dieter
Leithner to describe the problem of having to divide scarce time
between Life and real life.

:**LW volcano** = toaster

:**mango** (p1)

:**mathematician** (p5) Found by Dave Buckingham, 1972.

:**Max** A name for the smallest known spacefiller. The name represents
the fact that the growth rate is the fastest possible. (This has not
quite been proved, however. There remains the possibility, albeit
not very likely, that a periodic agar could have an average
density greater than 1/2, and a spacesfiller stretching such an
agar at the same speed as the known spacefillers would have a faster
average growth rate.)

:**mazing** (p4) In terms of its minimum population of 12 this ties with
mold as the smallest p4 oscillator. Found by Dave Buckingham in
December 1973. For some constructions using mazings, see popover
and sixty-nine.

:**medium fish** = MWSS

:**metacatacryst** A 52-cell pattern exhibiting quadratic growth. Found
by Nick Gotts, December 2000. This is currently the smallest known
pattern (in terms of initial population) with superlinear growth.
See also catacryst.

:**metamorphosis** An oscillator built by Robert Wainwright that uses
the following reaction (found by Bill Gosper) to turn gliders into
LWSS, and converts these LWSS back into gliders by colliding them
head on. (There are in fact two ways to do the following reaction,
because the spark of the twin bees shuttle is symmetric.)

:**metamorphosis II** An oscillator built by Robert Wainwright in
December 1994 based on the following p30 glider-to-LWSS
converter. This converter was first found by Paul Rendell,
January 1986 or earlier, but wasn't widely known about until
Paul Callahan rediscovered it in December 1994.

:**methuselah** Any small pattern that stabilizes only after a long
time. Term coined by Conway. Examples include the R-pentomino,
acorn and bunnies.

:**Mickey Mouse** (p1) A name proposed by Mark Niemiec for the following
still life:

:**middleweight emulator** = MW emulator

:**middleweight spaceship** = MWSS

:**middleweight volcano** = MW volcano

:**mini pressure cooker** (p3) Found by Robert Wainwright before
June 1972. Compare pressure cooker.

:**M.I.P. value** The maximum population divided by the initial
population for an unstable pattern. For example, the
R-pentomino has an M.I.P. value of 63.8, since its maximum
population is 319. The term is no longer in use.

:**MIT oscillator** = cuphook

:**MMM breeder** See breeder.

:**MMS breeder** See breeder.

:**mod** The smallest number of generations it takes for an
oscillator or spaceship to reappear in its original form,
possibily subject to some rotation or reflection. The mod may
be equal to the period, but it may also be a quarter of the period
(for oscillators that rotate 90 degrees every quarter period) or half
the period (for other oscillators which rotate 180 degrees every half
period, and also for flippers).

:**mold** (p4) Found by Achim Flammenkamp in 1988, but not widely known
until Dean Hickerson rediscovered it (and named it) in August 1989.
Compare with jam. In terms of its minimum population of 12 it
ties with mazing as the smallest p4 oscillator. But in terms
of its 6×6 bounding box it wins outright. In fact, of all
oscillators that fit in a 6×7 box it is the only one with period
greater than 2.

:**monogram** (p4) Found by Dean Hickerson, August 1989.

:**moose antlers** (p1)

:**mosquito** See mosquito1, mosquito2. mosquito3, mosquito4 and
mosquito5.

:**mosquito1** A breeder constructed by Nick Gotts in September 1998.
The original version had an initial population of 103, which was
then the smallest for any known pattern with superlinear growth
(beating the record previously held by Jaws). This was reduced
to 97 by Stephen Silver the following month, but was then almost
immediately superceded by mosquito2.

Mosquito1 consists of the classic puffer train plus four LWSS and four MWSS (mostly in predecessor form, to keep the population down). Once it gets going it produces a new block-laying switch engine (plus a lot of junk) every 280 generations. It is therefore an MMS breeder, albeit a messy one.

:**mosquito2** A breeder constructed by Nick Gotts in October 1998.
Its initial population of 85 was for a couple of hours the smallest
for any known pattern with superlinear growth, but was then beaten by
mosquito3.

Mosquito2 is very like mosquito1, but uses two fewer MWSS and one more LWSS.

:**mosquito3** A breeder constructed by Nick Gotts in October 1998.
Its initial population of 75 was at the time the smallest for any
known pattern with superlinear growth, but was beaten a few days
later by mosquito4.

Mosquito3 has one less LWSS than mosquito2. It is somewhat different from the earlier mosquitos in that the switch engines it makes are glider-producing rather than block-laying.

:**mosquito4** A slightly improved version of mosquito3 which Stephen
Silver produced in October 1998 making use of another discovery of
Nick Gotts (September 1997): an 8-cell pattern that evolves into a
LWSS plus some junk. Mosquito4 is a breeder with an initial
population of 73, at the time the smallest for any known pattern
with superlinear growth, but superceded a few days later by
mosquito5.

:**mosquito5** A slightly improved version of mosquito4 which Nick Gotts
produced in October 1998. The improvement is of a similar nature
to the improvement of mosquito4 over mosquito3. Mosquito5 is a
breeder with an initial population of 71. At the time, this was
the smallest population for any known pattern with superlinear
growth, but it has since been superceded by teeth, catacryst and
metacatacryst.

:**mould** = mold

:**MSM breeder** See breeder.

:**multi-state Life** = colorized Life

:**multum in parvo** (stabilizes at time 3933) A methuselah found by
Charles Corderman, but not as long-lasting as his acorn.

:**muttering moat** Any oscillator whose rotor consists of a closed
chain of cells each of which is adjacent to exactly two other rotor
cells. Compare babbling brook. Examples include the bipole,
the blinker, the clock, the cuphook, the Gray counter, the
quad, the scrubber, the skewed quad and the p2 snake pit.
The following diagram shows a p2 example (by Dean Hickerson, May
1993) with a larger rotor. See ring of fire for a very large one.

:**MW emulator** (p4) Found by Robert Wainwright in June 1980. See also
emulator and filter.

:**MWSS** (*c*/2 orthogonally, p4) The third most common spaceship.
Found by Conway in 1970.

:**MWSS emulator** = MW emulator

:**MWSS out of the blue** The following reaction, found by Peter Rott
in November 1997, in which a LWSS passing by a p46 oscillator
creates a MWSS travelling in the opposite direction. Together
with some reactions found by Dieter Leithner, and a LWSS-turning
reaction which Rott had found in November 1993 (but which was not
widely known until Paul Callahan rediscovered it in June 1994)
this can be used to prove that there exist gliderless guns for
LWSS, MWSS and HWSS for every period that is a multiple of 46.

:**MW volcano** (p5) Found by Dean Hickerson in April 1992.

:**My Experience with B-heptominos in Oscillators** An article by
Dave Buckingham (October 1996) that describes his discovery of
Herschel conduits, including sufficient (indeed ample) stable
conduits to enable, for the first time, the construction of period *n*
oscillators - and true period *n* guns - for every sufficiently large
integer *n*. (See Herschel loop and emu.)

:**natural** Occurring often in random patterns. There is no precise
measure of naturalness, since the most useful definition of "random"
in this context is open to debate. Nonetheless, it is clear that
objects such as blocks, blinkers, beehives and gliders are
very natural, while eater2s, darts, guns, etc., are not.

:**negentropy** (p2) Compare Hertz oscillator.

:**neighbour** Any of the eight cells adjacent to a given cell. A cell
is therefore not considered to be a neighbour of itself, although
the neighbourhood used in Life does in fact include this cell (see
cellular automaton).

:**new five** (p3) Found by Dean Hickerson, January 1990.

:**new gun** An old name for the second known basic gun (found, like
the first, by Bill Gosper), shown below. A number of other ways of
constructing a gun from two twin bees shuttles have since been
found - see edge shooter for one of these.

:**Noah's ark** The following diagonal puffer consisting of two
switch engines. This was found by Charles Corderman in 1971.
The name comes from the variety of objects it leaves behind: blocks,
blinkers, beehives, loaves, gliders, ships, boats, long boats,
beacons and block on tables.

:**n-omino** Any polyomino with exactly *n* cells.

:**non-monotonic** A spaceship is said to be non-monotonic if its
leading edge falls back in some generations. The first example
(shown below) was found found by Hartmut Holzwart in August 1992.
This is p4 and travels at *c*/4. In April 1994, Holzwart found
examples of p3 spaceships with this property, and this is clearly
the smallest possible period. Another non-monotonic spaceship is
the weekender.

:**non-spark** Something that looks like a spark, but isn't. An OWSS
produces one of these instead of a belly spark, and is destroyed
by it.

:**non-standard spaceship** Any spaceship other than a glider, LWSS,
MWSS or HWSS.

:**obo spark** A spark of the form `O.O` (so called after its rle
encoding).

:**octagon II** (p5) The first known p5 oscillator, discovered in 1971
independently by Sol Goodman and Arthur Taber. The name is due to
the latter.

:**octagon IV** (p4) Found by Robert Wainwright, January 1979.

:**octomino** Any 8-cell polyomino. There are 369 such objects. The
word is particularly applied to the following octomino (or its
two-generation successor), which is fairly common but lacks a proper
name:

:**odd keys** (p3) Found by Dean Hickerson, August 1989. See also
short keys and bent keys.

:**omino** = polyomino

:**omniperiodic** A cellular automaton is said to be
omniperiodic if it has oscillators of all periods.
It is not known if Life is omniperiodic, although this seems
likely. Dave Buckingham's work on Herschel conduits in 1996
(see My Experience with B-heptominos in Oscillators)
reduced the number of unresolved cases to a finite number.
At the time of writing the only periods for which no oscillator is
known are 19, 23, 31, 37, 38, 41, 43 and 53. If we insist that the
oscillator must contain a cell oscillating at the full period, then
34 and 51 should be added to this list. The most recently achieved
periods were all found by Noam Elkies: p49 in August 1999 (a glider
loop using p7 reflectors built from his new p7 pipsquirter),
p39 (previously only possible without a p39 cell) in July 2000, and
p27 in November 2002.

:**onion rings** For each integer *n*>1 onion rings of order *n* is a stable
agar of density 1/2 obtained by tiling the plane with a certain
4*n* × 4*n* pattern. The tile for order 3 onion rings is shown below -
the reader should then be able to deduce the form of tiles of other
orders.

:**on-off** Any p2 oscillator in which all rotor cells die from
overpopulation. The simplest example is a beacon. Compare
flip-flop.

:**O-pentomino** Conway's name for the following pentomino, a
traffic light predecessor, although not one of the more
common ones.

:**Orion** (*c*/4 diagonally, p4) Found by Hartmut Holzwart, April 1993.

:**orphan** Conway's preferred term for a Garden of Eden.

:**oscillator** Any pattern that is a predecessor of itself. The term
is usually restricted to non-stable finite patterns. An oscillator
is divided into a rotor and a stator. See also omniperiodic.

In general cellular automaton theory the term "oscillator" usually covers spaceships as well, but this usage is not normal in Life.

:**overcrowding** = overpopulation

:**over-exposure** = underpopulation

:**overpopulation** Death of cell caused by it having more than three
neighbours.

:**overweight spaceship** = OWSS

:**OWSS** A would-be spaceship similar to LWSS, MWSS and HWSS but
longer. On its own an OWSS is unstable, but it can be escorted by
true spaceships to form a flotilla.

:**Ox** A 1976 novel by Piers Anthony which involves Life.

:**p** = period

:**p30 shuttle** = queen bee shuttle

:**p46 shuttle** = twin bees shuttle

:**p54 shuttle** (p54) A surprising variant of the twin bees shuttle
found by Dave Buckingham in 1973. See also centinal.

:**pair of bookends** = bookends

:**pair of tables** = table on table

:**paperclip** (p1)

:**parent** A pattern is said to be a parent of the pattern it gives
rise to after one generation. Some patterns have infinitely many
parents, but other have none at all (see Garden of Eden).

:**parent cells** The three cells that cause a new cell to be born.

:**PD** = pentadecathlon

:**pedestle** (p5)

:**penny lane** (p4) Found by Dave Buckingham, 1972.

:**pentadecathlon** (p15) Found in 1970 by Conway while tracking the
history of short rows of cells, 10 cells giving this object, which is
the most natural oscillator of period greater than 3. In fact
it is the fifth or sixth most common oscillator overall, being
about as frequent as the clock, but much less frequent than the
blinker, toad, beacon or pulsar.

:**pentant** (p5) Found by Dave Buckingham, July 1976.

:**pentaplet** Any 5-cell polyplet.

:**pentapole** (p2) The barberpole of length 5.

:**pentoad** (p5) Found by Bill Gosper, June 1977. This is extensible:
if an eater is moved back four spaces then another Z-hexomino can
can be inserted. (This extensibility was discovered by Scott Kim.)

:**pentomino** Any 5-cell polyomino. There are 12 such patterns,
and Conway assigned them all letters in the range O to Z, loosely
based on their shapes. Only in the case of the R-pentomino
has Conway's label remained in common use, but all of them can
nonetheless be found in this lexicon.

:**period** The smallest number of generations it takes for an
oscillator or spaceship to reappear in its original form. The
term can also be used for a puffer, wick, fuse, superstring,
stream of spaceships, factory or gun. In the last case there
is a distinction between true period and pseudo period. There
is also a somewhat different concept of period for wicktrailers.

:**perturb** To change the fate of an object by reacting it with
other objects. Typically, the other objects are sparks from
spaceships or oscillators, or are eaters or impacting
spaceships. Perturbations are typically done to turn a dirty
reaction into a clean one, or to change the products of a reaction.
In many desirable cases the perturbing objects are not destroyed by
the reaction, or else are easily replenished.

:**perturbation** See perturb.

:**phase** A representative generation of a periodic object such as an
oscillator or spaceship. The number of phases is equal to the
period of the object. The phases of an object usually repeat in
the same cyclic sequence forever, although some perturbations can
cause a phase change.

:**phase change** A perturbation of a periodic object which causes the
object to skip ahead by one or more phases. If the perturbation
is repeated indefinitely, this can effectively change the period
of the object. An example of this, found by Dean Hickerson in
November 1998, is shown below. In this example, the period of the
oscillator would be 7 if the mold were removed, but the period
is increased to 8 because of the repeated phase changes caused by
the mold's spark.

Phase changing reactions have enabled the construction of spaceships having periods that were otherwise unknown, and also allow the construction of period-doubling and period-tripling convoys to easily produce very high period rakes.

See also blinker puffer.

:**phi** The following common spark. The name comes from the shape in
the generation after the one shown here.

:**phoenix** Any pattern all of whose cells die in every generation,
but which never dies as a whole. A spaceship cannot be a phoenix,
and in fact every finite phoenix eventually evolves into an
oscillator. The following 12-cell oscillator (found by the MIT
group in December 1971) is the smallest known phoenix, and is
sometimes called simply "the phoenix".

:**pi** = pi-heptomino

:**pi-heptomino** (stabilizes at time 173) A common pattern. The name is
also applied to later generations of this object - in a pi ship,
for example, the pi-heptomino itself never arises.

:**pincers** = great on-off

:**pinwheel** (p4) Found by Simon Norton, April 1970. Compare clock II.

:**pi orbital** (p168) Found by Noam Elkies, August 1995. In this
oscillator, a pi-heptomino is turned ninety degrees every 42
generations. A second pi can be inserted to reduce the period to 84.

:**pi portraitor** (p32) Found by Robert Wainwright in 1984 or 1985.
Compare with gourmet and popover.

:**pipsquirt** = pipsquirter

:**pipsquirter** An oscillator that produces a domino spark that
is orientated parallel to the direction from which it is produced
(in contrast to domino sparkers like the pentadecathlon and
HWSS, which produce domino sparks perpendicular to the direction
of production). The following is a small p6 example found by Noam
Elkies in November 1997.

:**pi ship** A growing spaceship in which the back part consists of
a pi-heptomino travelling at a speed of 3*c*/10. The first example
was constructed by David Bell. All known pi ships are too large to
show here, but the following diagram shows how the pi fuse works.

:**piston** (p2) Found in 1971.

:**pixel** = cell

:**plet** = polyplet

:**polyomino** A finite collection of orthogonally connected cells. The
mathematical study of polyominoes was initiated by Solomon Golomb
in 1953. Conway's early investigations of Life and other cellular
automata involved tracking the histories of small polyominoes,
this being a reasonable way to ascertain the typical behaviour of
different cellular automata when the patterns had to be evolved
by hand rather than by computer. Polyominoes have no special
significance in Life, but their extensive study during the early
years lead to a number of important discoveries and has influenced
the terminology of Life. (Note on spelling: As with "dominoes"
the plural may also be spelt without an e. In this lexicon I have
followed Golomb in using the longer form.)

It is possible for a polyomino to be an oscillator. In fact there are infinitely many examples of such polyominoes, namely the cross and its larger analogues. The only other known examples are the block, the blinker, the toad, the star and (in two different phases) the pentadecathlon.

A polyomino can also be a spaceship, as the LWSS, MWSS and HWSS show.

:**polyplet** A finite collection of orthogonally or diagonally connected
cells. This king-wise connectivity is a more natural concept in
Life than the orthogonal connectivity of the polyomino.

:**pond** (p1)

:**pond on pond** (p1) This term is often used to mean bi-pond, but may
also be used of the following pseudo still life.

:**popover** (p32) Found by Robert Wainwright in August 1984. Compare
with gourmet and pi portraitor.

:**population** The number of ON cells.

:**P-pentomino** Conway's name for the following pentomino, a common
spark.

:**PPS** (*c*/5 orthogonally, p30) A pre-pulsar spaceship. Any of three
different p30 *c*/5 orthogonal spaceships in which a pre-pulsar is
pushed by a pair of spiders. The back sparks of the spaceship can
be used to perturb gliders in many different ways, allowing the easy
construction of *c*/5 puffers. The first PPS was found by David Bell
in May 1998 based on a p15 pre-pulsar spaceship found by Noam Elkies
in December 1997. See also SPPS and APPS.

:**pre-beehive** The following common parent of the beehive.

:**pre-block** The following common parent of the block. Another
such pattern is the grin.

:**precursor** = predecessor

:**predecessor** Any pattern that evolves into a given pattern after
one or more generations.

:**pre-pulsar** A common predecessor of the pulsar, such as that
shown below. This duplicates itself in 15 generations. (It fails,
however, to be a true replicator because of the way the two copies
then interact.)

A pair of tubs can be placed to eat half the pre-pulsar as it replicates; this gives the p30 oscillator Eureka where the pre-pulsar's replication becomes a movement back and forth. (See twirling T-tetsons II for a variation on this idea.) By other means the replication of the pre-pulsar can be made to occur in just 14 generations as half of it is eaten; this allows the construction of p28 and p29 oscillators, and is in fact the only known method for creating a p29 oscillator. The pre-pulsar is also a vital component of the only known p47 oscillator.

See also PPS.

:**pre-pulsar spaceship** See PPS.

:**pressure cooker** (p3) Found by the MIT group in September 1971.
Compare mini pressure cooker.

:**primer** A pattern constructed by Dean Hickerson in November 1991 that
emits a stream of LWSSs representing the prime numbers.

:**protein** (p3) Found by Dave Buckingham, November 1972.

:**pseudo** Opposite of true. A gun emitting a period *n* stream of
spaceships (or rakes) is said to be a pseudo period *n* gun if its
mechanism oscillates with a period different from *n*. This period
will necessarily be a multiple of *n*. Pseudo period *n* glider guns
are known to exist for all periods greater than or equal to 14, with
smaller periods being impossible. The first pseudo p14 gun was built
by Dieter Leithner in 1995.

Exactly the same distinction between true and pseudo also exists for puffers.

:**pseudo-barberpole** (p5) Found by Achim Flammenkamp in August 1994.
In terms of its minimum population of 15 this is the smallest known
p5 oscillator.

:**pseudo-random glider generator** An object which emits a random-looking
stream of gliders, like the sequence of bits from a pseudo-random
number generator. Pseudo-random glider generators contain gliders
or other spaceships in a loop with a feedback mechanism which
causes later spaceships to interfere with the generation of earlier
spaceships. The period can be very high, since a loop of *n*
spaceships has 2^{n} possible states.

The first pseudo-random glider generator was built by Bill Gosper.
David Bell built the first moving one in 1997, using *c*/3 rakes.

:**pseudo still life** The strict definition of still life rules out
such stable patterns as the bi-block. In such patterns there are
dead cells which have more than 3 neighbours in total, but fewer than
3 in any component still life. These patterns are called pseudo
still lifes. Mark Niemiec has enumerated the pseudo still lifes
up to 24 bits, and his figures are shown below.

------------- Bits Number ------------- 8 1 9 1 10 7 11 16 12 55 13 110 14 279 15 620 16 1645 17 4067 18 10843 19 27250 20 70637 21 179011 22 462086 23 1184882 24 3068984 -------------

:**puffer** An object that moves like a spaceship, except that it
leaves debris behind. The first known puffers were found by Bill
Gosper and travelled at *c*/2 orthogonally (see diagram below for
the very first one, found in 1971). Not long afterwards *c*/12
diagonal puffers were found (see switch engine). Discounting
wickstretchers (which are not puffers in the conventional sense),
no new velocity was obtained after this until David Bell found the
first *c*/3 orthogonal puffer in April 1996. Since then *c*/5 orthogonal
puffers have also been found, the first by Tim Coe in May 1997.
Jason Summers built the first *c*/4 orthogonal puffer in January 1999,
and the first 2*c*/5 orthogonal puffer in February 1999.

:**puffer engine** A pattern which can be used as the main component of
a puffer. The pattern may itself be a puffer (e.g. the classic
puffer train), it may be a spaceship (e.g. the Schick engine),
or it may even be unstable (e.g. the switch engine).

:**puffer train** The full name for a puffer, coined by Conway before
any examples were known. The term was also applied specifically
to the classic puffer train found by Bill Gosper and shown below.
This is very dirty, and the tail does not stabilize until
generation 5533. It consists of a B-heptomino (shown here one
generation before the standard form) escorted by two LWSS. (This
was the second known puffer. The first is shown under puffer.)

:**puff suppressor** An attachment at the back of a line puffer that
suppresses all or some of its puffing action. The example below (by
Hartmut Holzwart) has a 3-cell puff suppressor at the back which
suppresses the entire puff, making a p2 spaceship. If you delete
this puff suppressor then you get a p60 double beehive puffer.
Puff suppressors were first recognised by Alan Hensel in April 1994.

:**pulsar** (p3) Despite its size, this is the fourth most common
oscillator (and by far the most common of period greater than 2)
and was found very early on by Conway. See also pre-pulsar and
pulsar quadrant.

:**pulsar 18-22-20** = two pulsar quadrants

:**pulsar CP 48-56-72** = pulsar (The numbers refer to the populations
of the three phases.)

:**pulsar quadrant** (p3) This consists of a quarter of the outer part of
a pulsar stabilized by a cis fuse with two tails. This is
reminiscent of mold and jam. Found by Dave Buckingham in July
1973. See also two pulsar quadrants.

:**pulse** A moving object, such as a spaceship or Herschel, which
can be used to transmit information. See pulse divider.

Also another name for a pulsar quadrant.

:**pulse divider** A mechanism that lets every *n*-th object that reaches
it pass through, and deletes all the rest, where *n* > 1 and the
objects are typically spaceships or Herschels.

The following diagram shows a p5 glider pulse divider by Dieter Leithner (February 1998). The first glider moves the centre block and is reflected at 90 degrees. The next glider to come along will not be reflected, but will move the block back to its original position. The small size and low period of this example make it useful for constructing glider guns of certain periods. p7, p22, p36 and p46 versions of this pulse divider are also known.

:**pulshuttle V** (p30) Found by Robert Wainwright, May 1985.
Compare Eureka.

:**pure glider generator** A pattern that evolves into one or more
gliders, and nothing else. There was some interest in these
early on, but they are no longer considered important. Here's
a neat example:

:**pushalong** Any tagalong at the front of a spaceship. The following
is an example (found by David Bell in 1992) attached to the front of
a MWSS.

:**pyrotechnecium** (p8) Found by Dave Buckingham in 1972.

:**pyrotechneczum** A common mistaken spelling of pyrotechnecium,
caused by a copying error in the early 1990s.

:**python** = long snake

:**Q** = Quetzal

:**Q-pentomino** Conway's name for the following pentomino, a
traffic light predecessor.

:**quad** (p2) Found by Robert Kraus, April 1971. Of all oscillators
that fit in a 6×6 box this is the only flipper.

:**QuadLife** A form of colorized Life in which there are four types of
ON cell. A newly-born cell takes the type of the majority of its
three parent cells, or the remaining type if its parent cells are
all of different types. In areas where there are only two types of
ON cell QuadLife reduces to Immigration.

:**quadpole** (p2) The barberpole of length 4.

:**quapole** = quadpole

:**quasar** (p3) Found by Robert Wainwright, August 1971. See pulsar.

:**queen bee** See queen bee shuttle.

:**queen bee shuttle** (p30) Found by Bill Gosper in 1970. There are a
number of ways to stabilize the ends. Gosper originally stabilized
shuttles against one another in a square of eight shuttles.
Two simpler methods are shown here; for a third see buckaroo.
The queen bee shuttle is the basis of all known true p30 guns
(see Gosper glider gun).

:**Quetzal** Dieter Leithner's name for the true p54 glider gun he built
in January 1998. (This is short for Quetzalcoatlus and expresses
the fact that the gun was a very large Herschel loop that was not
an emu.) Shortly afterwards Leithner also built a p56 Quetzal
using a mechanism found by Noam Elkies for this purpose. In October
1998 Stephen Silver constructed a p55 Quetzal using Elkies' p5
reflector of the previous month.

Some of the more recent Quetzals are not Herschel loops, but are instead short Herschel tracks firing several glider streams all but one of which is reflected back to the beginning of the track to create a new Herschel. Noam Elkies first had the idea of doing this for the p55 case, and Stephen Silver constructed the resulting gun shortly after building the original (much larger) p55 Quetzal. Jason Summers later built a p54 version, which is more complicated because the evenness of the period makes the timing problems considerably more difficult.

:**Quetzalcoatlus** A giant flying dinosaur after which Dieter Leithner
named his p54 gun. Usually abbreviated to Quetzal, or simply Q
(as in Q54, Q55, Q56, Q-gun, etc.).

:**quilt** = squaredance

:**R** = R-pentomino

:**R2D2** (p8) This was found, in the form shown below, by Peter Raynham
in the early 1970s. The name derives from a form with a larger
and less symmetric stator discovered by Noam Elkies in August
1994. Compare with Gray counter.

:**r5** = R-pentomino

:**rabbits** (stabilizes at time 17331) A methuselah found by Andrew
Trevorrow in 1986.

:**rake** Any puffer whose debris consists of spaceships. A rake is
said to be forwards, backwards or sideways according to the direction
of the spaceships relative to the direction of the rake. Originally
the term "rake" was applied only to forwards *c*/2 glider puffers (see
space rake). Many people prefer not to use the term in the case
where the puffed spaceships travel parallel or anti-parallel to the
puffer, as in this case they do not rake out any significant region
of the Life plane (and, in contrast to true rakes, these puffers
cannot travel in a stream, and so could never be produced by a
gun).

Although the first rakes (circa 1971) were *c*/2, rakes of other
velocities have since been built. Dean Hickerson's construction of
Corderships in 1991 made it easy for *c*/12 diagonal rakes to be
built, although no one actually did this until 1998, by which time
David Bell had constructed *c*/3 and *c*/5 rakes (May 1996 and September
1997, respectively). Jason Summers constructed a 2*c*/5 rake in June
2000 (building on work by Paul Tooke and David Bell) and a *c*/4
orthogonal rake in October 2000 (based largely on reactions found
by David Bell).

The smallest possible period for a rake is probably 7, as this
could be achieved by a 3*c*/7 orthogonal backwards glider puffer. The
smallest period attained to date is 8 (Jason Summers, March 2001) -
see backrake.

:**$rats** (p6) Found by Dave Buckingham, 1972.

:**R-bee** = bun

:**receiver** See Herschel receiver.

:**reflector** Any stable or oscillating pattern that can reflect some
type of spaceship (usually a glider) without suffering permanent
damage. The first known reflector was the pentadecathlon, which
functions as a 180-degree glider reflector (see relay). Other
examples include the buckaroo, the twin bees shuttle and some
oscillators based on the traffic jam reaction. Glider guns can
also be made into reflectors, although these are mostly rather large.

In September 1998 Noam Elkies found some fast small-period glider reflectors. The p8 version is shown below. Replacing the figure-8 by the p6 pipsquirter gives a p6 version. A more complicated construction allows a p5 version (which, as had been anticipated, soon led to a true p55 gun - see Quetzal). And in August 1999 Elkies found a suitable p7 sparker, allowing the first p49 oscillator to be constructed.

Stable reflectors are special in that if they satisfy certain conditions they can be used to construct oscillators of all sufficiently large periods. It was known for some time that stable reflectors were possible (see universal constructor), but no one was able to construct an explicit example until Paul Callahan did so in October 1996.

All known stable reflectors are very slow. Callahan's original reflector has a repeat time of 4840, soon improved to 1686 and then 894 and then 850. In November 1996 Dean Hickerson found a variant in which this is reduced to 747. Dave Buckingham reduced it to 672 in May 1997 using a somewhat different method, and in October 1997 Stephen Silver reduced it to 623 by a method closer to the original. In November 1998 Callahan reduced this to 575 with a new initial reaction. A small modification by Silver a few days later brought this down to 497.

But in April 2001 Dave Greene found a 180-degree stable reflector with a repeat time of only 202 (see boojum reflector). This reflector also won the $100 prize that Dieter Leithner had offered in April 1997 for the first stable reflector to fit in a 50×50 box, and the additional $100 that Alan Hensel had offered in January 1999 for the same feat. Dave Greene has subsequently offered $50 for the first 90-degree stable glider reflector that fits in a 50×50 box, and a further $50 for the first in a 35×35 box.

See also glider turner.

:**regulator** An object which converts input gliders aligned to some
period to output gliders aligned to a different period. The most
interesting case is a universal regulator.

:**relay** Any oscillator in which spaceships (typically gliders)
travel in a loop. The simplest example is the p60 one shown below
using two pentadecathlons. Pulling the pentadecathlons further
apart allows any period of the form 60+120*n* to be achieved - this
is the simplest proof of the existence of oscillators of arbitrarily
large period.

:**repeater** Any oscillator or spaceship.

:**repeat time** The minimum number of generations that is possible
between the arrival of one object and the arrival of the next. This
term is used for things such as reflectors or conduits and the
objects (gliders or Herschels, for example) will interact fatally
with each other (or one will interact fatally with a disturbance
caused by the other) if they are too close together. For example,
the repeat time of Dave Buckingham's 59-step B-heptomino to Herschel
conduit (shown under conduit) is 58.

:**rephaser** The following reaction that shifts the phase and path of
a pair of gliders. There is another form of this reaction that
reflects the gliders 180 degrees - see glider-block cycle.

:**replicator** A finite pattern which repeatedly creates
copies of itself. Such objects are known to exist (see
universal constructor), but no concrete example is known.

:**reverse fuse** A fuse that produces some initial debris, but then
burns cleanly. The following is a simple example.

:**revolver** (p2)

:**ring of fire** (p2) The following muttering moat found by Dean
Hickerson in September 1992.

:**rle** Run-length encoded. Run-length encoding is a simple (but not
very efficient) method of file compression. In Life the term refers
to a specific ASCII encoding used for Life patterns (and patterns
for other similar cellular automata). This encoding was introduced
by Dave Buckingham and is now the usual means of exchanging Life
patterns (especially large ones) by e-mail.

:**rock** Dean Hickerson's term for an eater which remains intact
throughout the eating process. The snake in Dave Buckingham's
59-step B-to-Herschel conduit (shown under conduit) is an
example. Other still lifes that sometimes act as rocks include the
tub, the hook with tail, the eater1 (eating with its tail)
and the hat (in Heinrich Koenig's stabilization of the
twin bees shuttle).

:**roteightor** (p8) Found by Robert Wainwright in 1972.

:**rotor** The cells of an oscillator that change state. Compare
stator. It is easy to see that any rotor cell must be adjacent
to another rotor cell.

:**R-pentomino** This is by far the most active polyomino with less
than six cells: all the others stabilize in at most 10 generations,
but the R-pentomino does not do so until generation 1103, by which
time it has a population of 116.

:**rule 22** Wolfram's rule 22 is the 2-state 1-D cellular automaton
in which a cell is ON in the next generation if and only if exactly
one of its three neighbours is ON in the current generation (a cell
being counted as a neighbour of itself). This is the behaviour of
Life on a cylinder of width 1.

:**rumbling river** Any oscillator in which the rotor is connected and
contained in a strip of width 2. The following p3 example is by Dean
Hickerson, November 1994.

:**S** Usually means big S, but may sometimes mean paperclip.

:**sailboat** (p16) A boat hassled by a Kok's galaxy, a figure-8
and two eater3s. Found by Robert Wainwright in June 1984.

:**sawtooth** Any finite pattern whose population grows without bound
but does not tend to infinity. (In other words, the population
reaches new heights infinitely often, but also infinitely often
drops below some fixed value.) The first such pattern was
constructed by Dean Hickerson in April 1991. Conway's preferred
plural is "sawteeth".

:**SBM** = sliding block memory

:**Schick engine** (*c*/2 orthogonally, p12) This spaceship, found by
Paul Schick in 1972, produces a large spark (the 15 live cells
at the rear in the phase shown below) which can be perturbed by
other *c*/2 spaceships to form a variety of puffers. The diagram
below shows the smallest form of the Schick engine, using two
LWSS. It is also possible to use two MWSS or two HWSS, or
even a LWSS and a HWSS.

:**Schick ship** = Schick engine

:**scorpion** (p1)

:**scrubber** (p2) Found in 1971.

:**SE** = switch engine

:**second glider domain** The second glider domain of an edge shooter
is the set of displacements (in space and time, relative to the
glider stream emitted by the edge shooter) that a glider stream
may have without interfering with the edge shooter. This is useful
to know, because edge shooters are often used to generate glider
streams very close to other glider streams.

:**sesquihat** (p1) Halfway between a hat and a twinhat.

:**SGR** Abbreviation for stable glider reflector.

:**shillelagh** (p1)

:**ship** (p1) The term is also used as a synonym of spaceship.

:**ship in a bottle** (p16) Found by Bill Gosper in August 1994.
See also bottle.

:**ship on boat** = ship tie boat

:**ship on ship** = ship-tie

:**ship-tie** (p1) The name is by analogy with boat-tie.

:**ship tie boat** (p1)

:**short keys** (p3) Found by Dean Hickerson, August 1989. See also
bent keys and odd keys.

:**shuttle** Any oscillator which consists of an active region moving
back and forth between stabilizing objects. The most well-known
examples are the queen bee shuttle (which has often been called
simply "the shuttle") and the twin bees shuttle. See also
p54 shuttle and Eureka. Another example is the p72 R-pentomino
shuttle that forms part of the pattern given under factory.

:**siamese** A term used in naming certain still lifes (and the stator
part of certain oscillators). It indicates that the object
consists of two smaller objects sharing two or more cells. See
snake siamese snake and loaf siamese barge for examples.

:**side** Half a sidewalk. In itself this is unstable and requires an
induction coil.

:**sidecar** A small tagalong for a HWSS that was found by Hartmut
Holzwart in 1992. The resulting spaceship (shown below) has a
phase with only 24 cells, making it in this respect the smallest
known spaceship other than the standard spaceships and some trivial
two-spaceship flotillas derived from them. Note also that a HWSS
can support two sidecars at once.

:**side-shooting gun** = slide gun

:**side-tracking** See universal constructor.

:**sidewalk** (p1)

:**siesta** (p5) Found by Dave Buckingham in 1973. Compare sombreros.

:**signal** Movement of information through the Life universe. Signals
can be carried by spaceships, fuses, drifters, or conduits.
Spaceships can only transfer a signal at the speed of the
spaceship, while fuses can transfer a signal at speeds up to the
speed of light.

In practice, many signals are encoded as the presence or absence of a glider (or other spaceship) at a particular point at a particular time. Such signals can be combined by the collision of gliders to form logic operations such as AND, OR, and NOT gates. Signals can be duplicated using glider duplicators or other fanout devices, and can be used up by causing perturbations on other parts of the Life object.

Signals are used in pseudo-random glider generators, the unit Life cell and the Fermat prime calculator, among others.

:**Silver's p5** (p5) The following oscillator found by Stephen Silver in
February 2000:

As this has no spark, it appears useless. Nonetheless, in March 2000, David Eppstein found a way to use it to reduce the size of Noam Elkies' p5 reflector.

:**singular flip flop** (p2) Found by Robert Wainwright, July 1972.

:**sinking ship** = canoe

:**six Ls** (p3) This is a compact form of loading dock.

:**sixty-nine** (p4) Found by Robert Wainwright, October 1978.

:**skewed quad** (p2)

:**skewed traffic light** (p3) Found by Robert Wainwright, August 1989.

:**slide gun** A gun which fires sideways from an extending arm. The
arm consists of streams of spaceships which are pushing a pattern
away from the body of the gun and releasing an output spaceship every
time they do so. Each output spaceship therefore travels along a
different path.

Dieter Leithner constructed the first slide gun in July 1994 (although he used the term "side shooting gun"). The following pattern shows the key reaction of this slide gun. The three gliders shown will push the block one cell diagonally, thereby extending the length of the arm by one cell, and at the same time they release an output glider sideways. (In 1999, Jason Summers constructed slide guns using other reactions.)

:**sliding block memory** A memory register whose value is stored as the
position of a block. The block can be moved by means of glider
collisions - see block pusher for an example.

In Conway's original formulation (as part of his proof of the existence of a universal computer in Life) 2 gliders were used to pull the block inwards by three diagonal spaces, and 30 gliders were used to push it out by the same amount. Dean Hickerson later greatly improved on this, finding a way to pull a block inwards by one diagonal space using 2 gliders, and push it out using 3 gliders. In order for the memory to be of any use there also has to be a way to read the value held. It suffices to be able to check whether the value is zero (as Conway did), or to be able to detect the transition from one to zero (as Hickerson did).

Dean Hickerson's sliding block memory is used in Paul Chapman's URM.

:**small fish** = LWSS

:**small lake** (p1) See also lake.

:**smiley** (p8) Found by Achim Flammenkamp in July 1994 and named
by Alan Hensel.

:**SMM breeder** See breeder.

:**smoke** Debris which is fairly long-lived but eventually dies
completely. Basically, a large spark. This term is used
especially when talking about the output from a spaceship -
see smoking ship.

:**smoking ship** A spaceship which produces smoke. If the smoke
extends past the edge of the rest of the spaceship, then it can be
used to perturb other objects as the spaceship passes by. Running
gliders into the smoke is often a good way to turn or duplicate the
them, or convert them into other objects. Sometimes the smoke from
a smoking ship may itself be perturbed by accompanying spaceships in
order to form a puffer. A simple example of a smoking ship is the
Schick engine.

:**snacker** (p9) Found by Mark Niemiec in 1972. This is a
pentadecathlon with stabilizers which force it into a lower period.

:**snail** (*c*/5 orthogonally, p5) The first known *c*/5 spaceship,
discovered by Tim Coe in January 1996. For some time it was the
slowest known orthogonal spaceship.

:**snake** (p1)

:**snake bit** An alternative name for a boat-bit. Not a very sensible
name, because various other things can be used instead of a snake.

:**snake bridge snake** (p1)

:**snake dance** (p3) Found by Robert Wainwright, May 1972.

:**snake pit** This term has been used for two different oscillators:
the p2 snake pit (essentially the same as fore and back)

:**snake siamese snake** (p1)

:**sombrero** One half of sombreros or siesta.

:**sombreros** (p6) Found by Dave Buckingham in 1972. If the two halves
are moved three spaces closer to one another then the period drops
to 4, and the result is just a less compact form of Achim's p4.
Compare also siesta.

:**soup** A random initial pattern, often assumed to cover the whole
Life universe.

:**space dust** A part of a spaceship or oscillator which looks like
a random mix of ON and OFF cells. It is usually very difficult to
find a glider synthesis for an object that consists wholly or
partly of space dust.

:**spacefiller** Any pattern that grows at a quadratic rate by filling
space with an agar. The first example was found in September 1993
by Hartmut Holzwart, following a suggestion by Alan Hensel. The
diagram below shows a smaller spacefiller found by Tim Coe. See also
Max. Spacefillers can be considered as breeders (more precisely,
MMS breeders), but they are very different from ordinary breeders.
The word "spacefiller" was suggested by Harold McIntosh and soon
became the accepted term.

:**space rake** The following p20 forwards glider rake, which was the
first known rake. It consists of an ecologist with a LWSS
added to turn the dying debris into gliders.

:**spaceship** Any finite pattern that reappears (without additions or
losses) after a number of generations and displaced by a non-zero
amount. By far the most natural spaceships are the glider,
LWSS, MWSS and HWSS. For further examples see big glider,
brain, Canada goose, Coe ship, Cordership, dart, dragon,
ecologist, edge-repair spaceship, Enterprise, flotilla,
fly, hammerhead, hivenudger, non-monotonic, Orion,
puff suppressor, pushalong, Schick engine, sidecar,
snail, still life tagalong, sparky, swan, turtle, wasp,
weekender and x66.

It is known that there exist spaceships travelling in all
rational directions and at arbitrarily slow speeds (see
universal constructor). Before 1989, however, the only known
examples travelled at *c*/4 diagonally (gliders) or *c*/2 orthogonally
(everything else). In 1989 Dean Hickerson started to use automated
searches to look for new spaceships, and had considerable success.
Other people have continued these searches using tools such as
lifesrc and gfind, and as a result we now have a great variety
of spaceships travelling at ten different velocities. The following
table details the discovery of spaceships with new velocities.

--------------------------------------------- Speed Direction Discoverer Date --------------------------------------------- c/4 diagonal Richard Guy 1970 c/2 orthogonal John Conway 1970 c/3 orthogonal Dean Hickerson Aug 1989 c/4 orthogonal Dean Hickerson Dec 1989 c/12 diagonal Dean Hickerson Apr 1991 2c/5 orthogonal Dean Hickerson Jul 1991 c/5 orthogonal Tim Coe Jan 1996 2c/7 orthogonal David Eppstein Jan 2000 c/6 orthogonal Paul Tooke Apr 2000 c/5 diagonal Jason Summers Nov 2000 ---------------------------------------------

In addition, Jason Summers has put together a fairly detailed
description of how to build a 17*c*/45 spaceship, although the
construction has not yet been carried out. See 17c/45 spaceship
for more details.

A period *p* spaceship which displaces itself (*m*,*n*) during its
period, where *m*>=*n*, is said to be of type (*m*,*n*)/*p*. It was proved by
Conway in 1970 that *p*>=2*m*+2*n*. (This follows immediately from the
easily-proved fact that a pattern cannot advance diagonally at a rate
greater than one half diagonal step every other generation.)

The following diagram shows the only known *c*/5 diagonal spaceship
(Jason Summers, November 2000).

:**Spaceships in Conway's Life** A series of articles posted by David
Bell to the newsgroup comp.theory.cell-automata during the period
August-October 1992 that described many of the new spaceships found
by himself, Dean Hickerson and Hartmut Holzwart. Bell produced an
addendum covering more recent developments in 1996.

:**spark** A pattern that dies. The term is typically used to describe
a collection of cells periodically thrown off by an oscillator or
spaceship, but other dying patterns, particulary those consisting
or only one or two cells (such as produced by certain glider
collisions, for example), are also described as sparks. For
examples of small sparks see unix and HWSS. For an example
of a much larger spark see Schick engine.

:**spark coil** (p2) Found in 1971.

:**sparker** An oscillator or spaceship that produces sparks.
These can be used to perturb other patterns without being
themselves affected.

:**sparky** A certain *c*/4 tagalong, shown here attached to the back
of a spaceship.

:**sparse Life** This refers to the study of the evolution of a
Life universe which starts off as a random soup of extremely
low density. Such a universe is dominated at an early stage
by blocks and blinkers (often referred to collectively
as blonks) in a ratio of about 2:1. Much later it will be
dominated by simple infinite growth patterns (presumably mostly
switch engines). The long-term fate of a sparse Life universe is
less certain. It may possibly become dominated by self-reproducing
patterns (see universal constructor), but it is not at all clear
that there is any mechanism for these to deal with the all junk
produced by switch engines.

:**speed of light** A speed of one cell per generation, the greatest
speed at which any effect can propagate.

:**S-pentomino** Conway's name for the following pentomino, which
rapidly dies.

:**spider** (*c*/5 orthogonally, p5) This is the smallest known *c*/5
spaceship, and was found by David Bell in April 1997. Its
side sparks have proved very useful in constructing *c*/5
puffers, including rakes. See also pre-pulsar.

:**spiral** (p1) Found by Robert Wainwright in 1971.

:**SPPS** (*c*/5 orthogonally, p30) The symmetric PPS. The original PPS
found by David Bell in May 1998. Compare APPS.

:**squaredance** The p2 agar formed by tiling the plane with the
following pattern. Found by Don Woods in 1971.

:**squirter** = pipsquirter

:**S-spiral** = big S

:**stable** A pattern is said to be stable if it is a parent of itself.
See still life.

:**stairstep hexomino** (stabilizes at time 63) The following
predecessor of the blockade.

:**stamp collection** A collection of oscillators (or perhaps other
Life objects) in a single diagram, displaying the exhibits much like
stamps in a stamp album. The classic examples are by Dean Hickerson
(see http://www.math.ucdavis.edu/~dean/RLE/stamps.html).

:**standard spaceship** A glider, LWSS, MWSS or HWSS. These have
all been known since 1970.

:**star** (p3) Found by Hartmut Holzwart, February 1993.

:**star gate** A device by Dieter Leithner (October 1996) for transporting
a LWSS faster than the speed of light. The key reaction is the
Fast Forward Force Field.

:**stator** The cells of an oscillator that are always on. Compare
rotor. (The stator is sometimes taken to include also some of
those cells which are always off.) The stator is divided into the
bushing and the casing.

By analogy, the cells of an eater that remain on even when the eater is eating are considered to constitute the stator of the eater. This is not necessarily well-defined, because the eater may have more than one eating action.

:**step** Another term for a generation. This term is particularly
used in describing conduits. For example, a 64-step conduit is
one through which the active object takes 64 generations to pass.

:**stillater** (p3) Found by Robert Wainwright, September 1985. This is
one of only three essentially different p3 oscillators with only
three cells in the rotor. The others are 1-2-3 and cuphook.

:**still life** Any stable pattern, usually assumed to be finite
and nonempty. For the purposes of enumerating still lifes this
definition is, however, unsatisfactory because, for example, any
pair of blocks would count as a still life, and there would therefore
be an infinite number of 8-bit still lifes. For this reason a
stricter definition is often used, counting a stable pattern as a
single still life only if its islands cannot be divided into two
nonempty sets both of which are stable in their own right. Compare
pseudo still life.

The requirement that a still life not be decomposable into two separate stable patterns may seem a bit arbitrary, as it does not rule out the possibility that it might be decomposable into more than two. This is shown by the patterns in the following diagram, both found by Gabriel Nivasch in July 2001. On the left is a 32-cell pattern that can be broken down into three stable pieces but not into two. On the right is a 34-cell pattern that can be broken down into four stable pieces but not into two or three. (Note that, as a consequence of the Four-Colour Theorem, four is as high as you need ever go.) It is arguable that patterns like these ought not to be considered as single still lifes.

Still lifes have been enumerated by Conway (4-7 bits), Robert Wainwright (8-10 bits), Dave Buckingham (11-13 bits), Peter Raynham (14 bits) and Mark Niemiec (15-24 bits). The resulting figures are shown below. (These figures shouldn't be affected by the above discussion of the strict definition of "still life", because it is unlikely that there are any doubtful cases with much less than 32 cells.)

------------- Bits Number ------------- 4 2 5 1 6 5 7 4 8 9 9 10 10 25 11 46 12 121 13 240 14 619 15 1353 16 3286 17 7773 18 19044 19 45759 20 112243 21 273188 22 672172 23 1646147 24 4051711 -------------

:**still life tagalong** A tagalong which takes the form of a
still life in at least one phase. An example is shown below.

:**stretcher** Any pattern that grows by stretching a wick or agar.
See wickstretcher and spacefiller.

:**strict volatility** A term suggested by Noam Elkies in August 1998
for the proportion of cells involved in a period *n* oscillator which
themselves oscillate with period *n*. For prime *n* this is the same
as the ordinary volatility.

:**super beehive** = honeycomb

:**superfountain** (p4) This sparker was found by Noam Elkies in
February 1998 (shown here with a slightly smaller stator).
The resulting spark is more isolated than in the fountain.

:**superstring** An infinite orthogonal row of cells stabilized on one
side so that it moves at the speed of light, often leaving debris
behind. The first examples were found in 1971 by Edward Fitzgerald
and Robert Wainwright. Superstrings were studied extensively
by Peter Rott during 1992-1994, and he found examples with many
different periods. (But no odd periods. In August 1998 Stephen
Silver proved that odd-period superstrings are impossible.)

Sometimes a finite section of a superstring can be made to run between two tracks ("waveguides"). This gives a fuse which can be made as wide as desired. The first example was found by Tony Smithurst and uses tubs. (This is shown below. The superstring itself is p4 with a repeating section of width 9 producing one blinker per period and was one of those discovered in 1971. With the track in place, however, the period is 8. This track can also be used with a number of other superstrings.) Shortly after seeing this example, in March 1997 Peter Rott found another superstring track consisting of boats. At present these are the only two waveguides known. Both are destroyed by the superstring as it moves along - it would be interesting to find one that remains intact.

See titanic toroidal traveler for another example of a superstring.

:**support** Those parts of an object which are only present in order to
keep the rest of the object (such an engine or an edge spark)
working correctly. These can be components of the object, or else
accompanying objects used to perturb the object. In many cases
there is a wide variation of support possible for an engine. The
arms in many puffers are an example of support.

:**surprise** (p3) Found by Dave Buckingham, November 1972.

:**swan** (*c*/4 diagonally, p4) A diagonal spaceship producing some
useful sparks (see boatstretcher for one simple use). Found
by Tim Coe in February 1996.

:**switch engine** The following pattern, which in itself is unstable,
but which can be used to make *c*/12 diagonal puffers and
spaceships.

The switch engine was discovered by Charles Corderman in 1971. He also found the two basic types of stabilized switch engine: a p288 block-laying type (the more common of the two) and p384 glider-producing type. These two puffers are the most natural infinite growth patterns in Life, being the only ones ever seen to occur from random starting patterns.

Patterns giving rise to block-laying switch engines can be seen under infinite growth, and one giving rise to a glider-producing switch engine is shown under time bomb. See also Cordership and ark.

:**synthesis** = glider synthesis

:**T** = T-tetromino

:**table** The following induction coil.

:**table on table** (p1)

:**tag** = tagalong

:**tagalong** An object which is not a spaceship in its own right, but
which can be attached to one or more spaceships to form a larger
spaceship. For examples see Canada goose, fly, pushalong,
sidecar and sparky. See also Schick engine, which consists of
a tagalong attached to two LWSS (or similar).

:**tail spark** A spark at the back of a spaceship. For example, the
1-bit spark at the back of a LWSS, MWSS or HWSS in their less
dense phases.

:**tame** To perturb a dirty reaction using other patterns so as to
make it clean and hopefully useful. Or to make a reaction work
which would otherwise fail due to unwanted products which interfere
with the reaction.

:**taming** See tame.

:**teardrop** The following induction coil, or the formation of two
beehives that it evolves into after 20 generations. (Compare
butterfly, where the beehives are five cells further apart.)

:**technician** (p5) Found by Dave Buckingham, January 1973.

:**technician finished product** = technician

:**teeth** A 65-cell quadratic growth pattern found by Nick Gotts in March
2000. This (and a related 65-cell pattern which Gotts found at about
the same time) beat the record previously held by mosquito5 for
smallest population known to have superlinear growth. Now superceded
by catacryst and metacatacryst.

:**ternary reaction** Any reaction between three objects. In particular,
a reaction in which two gliders from one stream and one glider from
a crossing stream of the same period annihilate each other. This
can be used to combine two glider guns of the same period to produce
a new glider gun with double the period.

:**test tube baby** (p2)

:**tetraplet** Any 4-cell polyplet.

:**tetromino** Any 4-cell polyomino. There are five such objects,
shown below. The first is the block, the second is the
T-tetromino and the remaining three rapidly evolve into
beehives.

:**The Recursive Universe** A popular science book by William
Poundstone (1985) dealing with the nature of the universe,
illuminated by parallels with the game of Life. This book
brought to a wider audience many of the results that first
appeared in LifeLine. It also outlines the proof of the
existence of a universal constructor in Life first given
in Winning Ways.

:**thumb** A spark-like protrusion which flicks out in a manner
resembling a thumb being flicked.

Here are two examples. On the left is a p9 thumb sparker found by Dean Hickerson in October 1998. On the right is a p4 one found by David Eppstein in June 2000.

:**thunderbird** (stabilizes at time 243)

:**tick** = generation

:**tie** A term used in naming certain still lifes (and the stator
part of certain oscillators). It indicates that the object
consists of two smaller objects joined point to point, as in
ship tie boat.

:**time bomb** The following pattern by Doug Petrie, which is really
just a glider-producing switch engine in disguise. See
infinite growth for some better examples of a similar nature.

:**titanic toroidal traveler** The superstring with the following
repeating segment. The front part becomes p16, but the eventual
fate of the detatched back part is unknown.

:**TL** = traffic light

:**T-nosed p4** (p4) Found by Robert Wainwright in October 1989. See also
filter.

:**T-nosed p6** (p6) Found by Achim Flammenkamp in September 1994.
There is also a much larger and fully symmetric version found
by Flammenkamp in August 1994.

:**toad** (p2) Found by Simon Norton, May 1970. This is the second most
common oscillator, although blinkers are more than a hundred
times as frequent. See also killer toads.

:**toad-flipper** A toad hassler that works in the manner of the
following example. Two domino sparkers, here pentadecathlons,
apply their sparks to the toad in order to flip it over. When the
sparks are applied again it is flipped back. Either or both domino
sparkers can be moved down two spaces from the position shown and
the toad-flipper will still work, but because of symmetry there are
really only two different types. Compare toad-sucker.

:**toad-sucker** A toad hassler that works in the manner of the
following example. Two domino sparkers, here pentadecathlons,
apply their sparks to the toad in order to shift it. When the
sparks are applied again it is shifted back. Either or both domino
sparkers can be moved down two spaces from the position shown and the
toad-sucker will still work, but because of symmetry there are really
only three different types. Compare toad-flipper.

:**toaster** (p5) Found by Dean Hickerson, April 1992.

:**torus** As applies to Life, usually means a finite Life universe
which takes the form of an *m* × *n* rectangle with the bottom edge
considered to be joined to the top edge and the left edge joined
to the right edge, so that the universe is topologically a torus.
There are also other less obvious ways of obtaining an toroidal
universe.

See also Klein bottle.

:**total aperiodic** Any finite pattern which evolves in such a way that
no cell in the Life plane is eventually periodic. The first example
was found by Bill Gosper in November 1997. A few days later he found
the following much smaller example consisting of three copies of a
p12 backrake by Dave Buckingham.

:**T-pentomino** Conway's name for the following pentomino, which is a
common parent of the T-tetromino.

:**track** A path made out of conduits, often ending where it begins
so that the active object is cycled forever, forming an oscillator
or a gun.

:**traffic circle** (p100)

:**traffic jam** Any traffic light hassler, such as traffic circle.
The term is also applied to the following reaction, used in most
traffic light hasslers, in which two traffic lights interact in such
a way as to reappear after 25 generations with an extra 6 spaces
between them.

:**traffic light** (p2) A common formation of four blinkers.

:**trans-beacon on table** (p2)

:**trans-boat with tail** (p1)

:**transceiver** See Herschel transceiver.

:**trans-loaf with tail** (p1)

:**transmitter** See Herschel transmitter.

:**transparent block reaction** A certain reaction between a block and
a Herschel predecessor in which the block reappears in its
original place some time later, the reaction having effectively
passed through it. This reaction was found by Dave Buckingham in
1988. It has been used in some Herschel conduits, and in the
gunstars. Because the reaction involves a Herschel predecessor
rather than an actual Herschel, the following diagram shows instead
a B-heptomino (which by itself would evolve into a block and a
Herschel).

:**transparent debris effect** A reaction in which a Herschel or
other active region destroys a still life, then later, having
passed through the place where the still life was, recreates
the still life in its original position. For an example, see
transparent block reaction.

:**trice tongs** (p3) Found by Robert Wainwright, February 1982. In terms
of its 7×7 bounding box this ties with jam as the smallest p3
oscillator.

:**triomino** Either of the two 3-cell polyominoes. The term is
rarely used in Life, since the two objects in question are simply
the blinker and the pre-block.

:**triple caterer** (p3) Found by Dean Hickerson, October 1989. Compare
caterer and double caterer.

:**triplet** Any 3-cell polyplet. There are 5 such objects, shown
below. The first two are the two triominoes, and the other three
vanish in two generations.

:**tripole** (p2) The barberpole of length 3.

:**tritoad** (p3) Found by Dave Buckingham, October 1977.

:**true** Opposite of pseudo. A gun emitting a period *n* stream of
spaceships (or rakes) is said to be a true period *n* gun if
its mechanism oscillates with period *n*. (The same distinction
between true and pseudo also exists for puffers.) True period
*n* guns are known to exist for all periods greater than 61 (see
My Experience with B-heptominos in Oscillators), but only a
few smaller periods have been achieved, namely 22, 24, 30, 44,
46, 48, 50, 54, 55, 56 and 60. (Credits for these small period
guns are: p30, p46 and p60 by Bill Gosper in 1970-1971, p44 by
Dave Buckingham in 1992, p50 by Dean Hickerson in 1996, p24 and p48
by Noam Elkies in 1997, p54 and p56 by Dieter Leithner in early 1998,
p55 by Stephen Silver in late 1998 and p22 by David Eppstein in
2000.)

The following diagram shows the p22 gun (David Eppstein, August 2000, using two copies of a p22 oscillator found earlier the same day by Jason Summers).

:**T-tetromino** The following common predecessor of a traffic light.

:**tub** (p1)

:**tubber** (p3) Found by Robert Wainwright before June 1972..

:**tubstretcher** See boatstretcher.

:**tub with tail** (p1)

:**tugalong** = tagalong

:**tumbler** (p14) The smallest known p14 oscillator. Found by
George Collins in 1970.

:**tumbling T-tetson** (p8) A T-tetromino hassled by two figure-8s.
Found by Robert Wainwright.

:**Turing machine** See universal computer.

:**turning toads** (p4 wick) Found by Dean Hickerson, October 1989.

:**turtle** (*c*/3 orthogonally, p3) Found by Dean Hickerson.

:**twin bees shuttle** (p46) Found by Bill Gosper in 1971, this is the
basis of all known p46 oscillators, and so of all known true p46
guns (see new gun for an example). There are numerous ways to
stabilize the ends, two of which are shown in the diagram. On the
left is David Bell's double block reaction (which results in a
shorter, but wider, shuttle than usual), and on the right is the
stabilization by a single block. This latter method produces a
very large spark which is useful in a number of ways (see, for
example, metamorphosis). Adding a symmetrically placed block
below this one suppresses the spark. See also p54 shuttle.

:**twinhat** (p1) See also hat and sesquihat.

:**twin peaks** = twinhat

:**twirling T-tetsons II** (p60) Found by Robert Wainwright. This is
a pre-pulsar hassled by killer toads.

:**two eaters** (p3) Found by Bill Gosper, September 1971.

:**two pulsar quadrants** (p3) Found by Dave Buckingham, July 1973.
Compare pulsar quadrant.

:**underpopulation** Death of cell caused by it having fewer than two
neighbours.

:**unit Life cell** A rectangular pattern, of size greater than 1×1,
that can simulate Life in the following sense. The pattern
by itself represents a dead Life cell, and some other pattern
represents a live Life cell. When the plane is tiled by these
two patterns (which then represent the state of a whole Life
universe) they evolve, after a fixed amount of time, into another
tiling of the plane by the same two patterns which correctly
represents the Life generation following the one they initially
represented. It is usual to use capital letters for the simulated
things, so, for example, for the first known unit Life cell
(constructed by David Bell in January 1996), one Generation is
5760 generations, and one Cell is 500×500 cells.

:**universal computer** A computer that can compute anything that is
computable. (The concept of computability can be defined in terms
of Turing machines, or by Church's lambda calculus, or by a number
of other methods, all of which can be shown to lead to equivalent
definitions.) The relevance of this to Life is that both Bill
Gosper and John Conway proved early on that it is possible to
construct a universal computer in the Life universe. (To prove
the universality of a cellular automaton with simple rules was
in fact Conway's aim in Life right from the start.) Conway's proof
is outlined in Winning Ways, and also in The Recursive Universe.

Until recently, no universal Life computer had ever been built in practice, because it would be enormous, even with the improvements that have been devised since those early proofs. In April 2000, Paul Rendell completed a Turing machine construction which can be seen at http://rendell.server.org.uk/gol/tm.htm. This, however, has a finite tape, as opposed to the infinite tape of a true Turing machine, and is therefore not a universal computer. But in November 2002, Paul Chapman announced the construction of a universal computer, details of which can be found at http://www.igblan.com/ca/. This is a universal register machine based around Dean Hickerson's sliding block memory.

See also universal constructor.

:**universal constructor** A pattern that is capable of constructing
almost any pattern that has a glider synthesis. This definition is
a bit vague. A precise definition seems impossible because it has
not been proved that all possible glider fleets are constructible.
In any case, a universal constructor ought to be able to construct
itself in order to qualify as such. An outline of Conway's proof
that such a pattern exists can be found in Winning Ways, and also
in The Recursive Universe. The key mechanism for the production
of gliders with any given path and timing is known as side-tracking,
and is based on the kickback reaction. A universal constructor
designed in this way can also function as a universal destructor
- it can delete almost any pattern that can be deleted by gliders.

A universal constructor is most useful when attached to a universal computer, which can be programmed to control the constructor to produce the desired pattern of gliders. In what follows I will assume that a universal constructor always includes this computer.

The existence of a universal constructor/destructor has a number of theoretical consequences.

For example, the constructor could be programmed to make copies of itself. This is a replicator.

The constructor could even be programmed to make just one copy of itself translated by a certain amount and then delete itself. This would be a (very large, very high period) spaceship. Any translation is possible (except that it must not be too small), so that the spaceship could travel in any direction. It could also travel slower than any given speed, since we could program it to perform some time-wasting task (such as repeatedly constructing and deleting a block) before copying itself. Of course, we could also choose for it to leave some debris behind, thus making a puffer.

It is also possible to show that the existence of a universal constructor implies the existence of a stable reflector. This proof is not so easy, however, and is no longer of much significance now that explicit examples of such reflectors are known.

:**universal destructor** See universal constructor.

:**universal register machine** = URM

:**universal regulator** A regulator in which the incoming gliders are
aligned to period 1, that is, they have arbitrary timing (subject
to some minimum time required for the regulator to recover from the
previous glider).

Paul Chapman constructed the first universal regulator in March 2003. It is adjustable, so that the output can be aligned to any desired period.

:**unix** (p6) Two blocks eating a long barge. This is a useful
sparker, found by Dave Buckingham in February 1976. The name
derives from the fact that it was for some time the mascot of the
Unix lab of the mathematics faculty at the University of Waterloo.

:**up boat with tail** = trans-boat with tail

:**U-pentomino** Conway's name for the following pentomino, which
rapidly dies.

:**URM** A universal register machine, particularly Paul Chapman's
Life implementation of such a machine. See universal computer
for more information.

:**vacuum** Empty space. That is, space containing only dead cells.

:**Venetian blinds** The p2 agar obtained by using the pattern `O..O` to
tile the plane.

:**very long** = long long

:**very long house** The following induction coil.

:**volatility** The volatility of an oscillator is the size (in cells)
of its rotor divided by the sum of the sizes of its rotor and its
stator. In other words, it is the proportion of cells involved in
the oscillator which actually oscillate. For many periods there are
known oscillators with volatility 1, see for example Achim's p16,
figure-8, Kok's galaxy, mazing, pentadecathlon, phoenix,
relay, smiley and tumbler. The smallest period for which the
existence of such statorless oscillators is undecided is 3, although
Dean Hickerson showed in 1994 that there are p3 oscillators with
volatility arbitrarily close to 1 (as is the case for all but
finitely many periods, because of the possibility of feeding the
gliders from a true period *n* gun into an eater).

The term "volatility" is due to Robert Wainwright. See also strict volatility.

:**volcano** Any of a number of p5 oscillators which produce
sparks. See lightweight volcano, middleweight volcano
and heavyweight volcano.

:**V-pentomino** Conway's name for the following pentomino, a loaf
predecessor.

:**washerwoman** (2*c*/3 p18 fuse) A fuse by Earl Abbe.

:**washing machine** (p2) Found by Robert Wainwright before June 1972.

:**wasp** (*c*/3 orthogonally, p3) The following spaceship which produces
a domino spark at the back. It is useful for perturbing other
objects. Found by David Bell, March 1998.

:**wavefront** (p4) Found by Dave Buckingham, 1976 or earlier.

:**waveguide** See superstring.

:**weekender** (2*c*/7 orthogonally, p7) Found by David Eppstein in
January 2000. In April 2000 Stephen Silver found a tagalong for a
pair of weekenders. At present, *n* weekenders pulling *n*-1 tagalongs
constitute the only known spaceships of this speed or period.

:**weld** To join two or more still lifes or oscillators together.
This is often done in order to fit the objects into a smaller space
than would otherwise be possible. The simplest useful example is
probably the integral sign, which can be considered as a pair of
welded eater1s.

:**Wheels, Life, and other Mathematical Amusements** One of Martin
Gardner's books (1983) that collects together material from his
column in Scientific American. The last three chapters of this
book contain all the Life stuff.

:**why not** (p2) Found by Dave Buckingham, July 1977.

:**wick** A stable or oscillating linearly repeating pattern that can be
made to burn at one end. See fuse.

:**wickstretcher** A spaceship-like object which stretches a wick
that is fixed at the other end. The wick here is assumed to be
in some sense connected, otherwise most puffers would qualify as
wickstretchers. The first example of a wickstretcher was found in
October 1992 (front end by Hartmut Holzwart and back end by Dean
Hickerson) and stretches ants at a speed of *c*/4. This is shown
below with an improved back end found by Hickerson the following
month.

:**wicktrailer** Any extensible tagalong, that is, one which can
be attached to the back of itself, as well as to the back of a
spaceship. The number of generations which it takes for the
tagalong to occur again in the same place is often called the
period of the wicktrailer - this has little relation to the period
of the tagalong units themselves.

:**windmill** (p4) Found by Dean Hickerson, November 1989.

:**wing** The following induction coil. This is generation 2 of
block and glider.

:**WinLifeSearch** Jason Summers' GUI version of lifesrc for MS Windows.
It is available from http://entropymine.com/jason/life/software/.

:**Winning Ways** A two-volume book (1982) by Elwyn Berlekamp, John
Conway and Richard Guy on mathematical games. The last chapter
of the second volume concerns Life, and outlines a proof of the
existence of a universal constructor.

:**WLS** = WinLifeSearch

:**worker bee** (p9) Found by Dave Buckingham in 1972. Unlike the similar
snacker this produces no sparks, and so is not very important.
Like the snacker, the worker bee is extensible - it is, in fact, a
finite version of the infinite oscillator which consists of six ON
cells and two OFF cells alternating along a line. Note that Dean
Hickerson's new snacker ends also work here.

:**W-pentomino** Conway's name for the following pentomino, a common
loaf predecessor.

:**x66** (*c*/2 orthogonally, p4) Found by Hartmut Holzwart, July 1992.
Half of this can be escorted by a HWSS. The name refers to the
fact that every cell (live or dead) has at most 6 live neighbours
(in contrast to spaceships based on LWSS, MWSS or HWSS).
In fact this spaceship was found by a search with this restriction.

:**Xlife** A popular freeware Life program that runs under the X Window
System. The main Life code was written by Jon Bennett, and the X
code by Chuck Silvers.

:**X-pentomino** Conway's name for the following pentomino, a
traffic light predecessor.

:**Y-pentomino** Conway's name for the following pentomino, which
rapidly dies.

:**Z-hexomino** The following hexomino. The Z-hexomino features in
the pentoad, and also in Achim's p144.

:**Z-pentomino** Conway's name for the following pentomino, which
rapidly dies.

:**zweiback** (p30) An oscillator in which two HW volcanoes hassle a
loaf. This was found by Mark Niemiec in February 1995 and is too
big to show here.

David I. Bell, *Spaceships in Conway's Life*.
Series of articles posted on comp.theory.cell-automata,
Aug-Oct 1992. Now available from
his web-site.

David I. Bell, *Speed c/3 Technology in Conway's Life*,
17 December 1999. Available from
his web-site.

Elwyn R. Berlekamp, John H. Conway and Richard K. Guy,
*Winning Ways for your Mathematical Plays, II: Games in Particular*.
Academic Press, 1982.

David J Buckingham, *Some Facts of Life*. BYTE, December 1978.

Dave Buckingham, *My Experience with B-heptominos in Oscillators*.
12 October 1996.
Available
from Paul Callahan's web-site.

David J. Buckingham and Paul B. Callahan,
*Tight Bounds on Periodic Cell Configurations in Life*.
Experimental Mathematics 7:3 (1998) 221-241.
Available at
http://www.expmath.org/restricted/7/7.3/callahan.ps.gz.

Noam D. Elkies, *The still-Life density problem and its
generalizations*,
pp228-253 of "Voronoi's Impact on Modern Science,
Book I", P. Engel, H. Syta (eds), Institute of Mathematics, Kyiv 1998
= Vol.21 of Proc. Inst. Math. Nat. Acad. Sci. Ukraine,
math.CO/9905194.

Martin Gardner, *Wheels, Life, and other Mathematical Amusements*.
W. H. Freeman and Company, 1983.

R. Wm. Gosper, *Exploiting Regularities in Large Cellular Spaces*.
Physica 10D (1984) 75-80.

N. M. Gotts and P. B. Callahan, *Emergent structures in sparse fields of
Conway's 'Game of Life'*, in *Artificial Life VI: Procedings of the
Sixth International Conference on Artificial Life*, MIT Press, 1998.

Mark D Niemiec, *Life Algorithms*. BYTE, January 1979.

William Poundstone, *The Recursive Universe*.
William Morrow and Company Inc., 1985.

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