Life Lexicon (S)
Author: Stephen A. Silver
Description: Part of Stephen Silver's Life Lexicon.

Introduction | Bibliography

1-9 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z

: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.

    ........O...........O........
    .......O.O.........O.O.......
    ........O...........O........
    .............................
    ......OOOOO.......OOOOO......
    .....O....O.......O....O.....
    ....O..O.............O..O....
    .O..O.OO.............OO.O..O.
    O.O.O.....O.......O.....O.O.O
    .O..O....O.O.....O.O....O..O.
    ....OO..O..O.....O..O..OO....
    .........OO.......OO.........
    .............OO..............
    .............O.O.............
    ........O..O..O..............
    .......O.....................
    .....OO..........OOO.........
    ..O......OO.O....OOO.........
    .....O...O..O....OOO.........
    .....OOO.O...O......OOO......
    ..O...........O.....OOO......
    ...O...O.OOO........OOO......
    ....O..O...O.................
    ....O.OO......O..............
    ..........OO.................
    .........O...................
    .....O..O....................

: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 returns to some fixed value.) Conway's preferred plural is "sawteeth".

The first sawtooth was constructed by Dean Hickerson in April 1991. The least infinitely repeating population of any known sawtooth is 262 (David Bell, July 2005).

See also tractor beam.

: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.

    OOOO..............
    O...O.........O...
    O...........OO....
    .O..O..OO.....OOO.
    ......OOO......OOO
    .O..O..OO.....OOO.
    O...........OO....
    O...O.........O...
    OOOO..............

:Schick ship = Schick engine

:scorpion (p1)

    ...O...
    .OOO...
    O...OO.
    O.O.O.O
    .OO.O.O
    .....O.

:scrubber (p2) Found in 1971.

    ....O......
    ..OOO......
    .O.........
    .O..OOO....
    OO.O...O...
    ...O...O...
    ...O...O.OO
    ....OOO..O.
    .........O.
    ......OOO..
    ......O....

:SE = switch engine

:seal (c/6 diagonally, p6) The first c/6 diagonal spaceship, found by Nicolay Beluchenko in September 2005.

    ...O..OO..........................
    .OOO.O.O.O........................
    .O..OOO..OO.......................
    O..OOOOOO.O.OOO...................
    .O..OOO.O.OOOOO...................
    ......O.O.O.O.....................
    O.O...O.O.OOOOO...................
    O..O.O..O.OO...O..................
    ...O..OO.......OOO................
    .O...OOOOO.OOO..OO................
    ....O.........O...................
    ..O.O.........O...................
    ....OO.OOOOO...O..................
    ......O.OOO..O.....OO.............
    ......O..O...O.OOO.OO.............
    ........OO...OOO.O..O...O.........
    ........OO....OO.OOOO...OOO.......
    ...................O.O..O.........
    .............O.O.....OO..OO.......
    .............O..O.....O.OOO.....O.
    .............O...O....OO..O...O..O
    ...............OOO.....OO........O
    ...............O.O..O..O.....OO..O
    .................O..OO.OO.O..O....
    ................O.......O.O.......
    .................O...OOOO.........
    ..................O...O...........
    ..................................
    .......................O..........
    ......................O.O.........
    .....................OO...........
    .....................O.O..........
    .....................OO...........
    .......................O..........
    ......................O...........

: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.

    ....O
    OO.O.O.
    .O.O.O.
    .O.O.OO
    ..O...

:SGR Abbreviation for stable glider reflector.

:shillelagh (p1)

    OO...
    O..OO
    .OO.O

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

    OO.
    O.O
    .OO

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

    ....OO......OO....
    ...O..O....O..O...
    ...O.O......O.O...
    .OO..OOO..OOO..OO.
    O......O..O......O
    O.OO..........OO.O
    .O.O..........O.O.
    ...OO...OO...OO...
    .......O.O........
    .......OO.........
    ...OO........OO...
    .O.O..........O.O.
    O.OO..........OO.O
    O......O..O......O
    .OO..OOO..OOO..OO.
    ...O.O......O.O...
    ...O..O....O..O...
    ....OO......OO....

:ship on boat = ship tie boat

:ship on ship = ship-tie

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

    OO....
    O.O...
    .OO...
    ...OO.
    ...O.O
    ....OO

:ship tie boat (p1)

    OO....
    O.O...
    .OO...
    ...OO.
    ...O.O
    ....O.

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

    .O........O.
    O.OOO..OOO.O
    .O..O..O..O.
    ....O..O....

: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.

    OO...
    O.OOO
    ....O

: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.

    .O......
    O.....O.
    O.....O.
    OOOOO.O.
    ........
    ....OO..
    ..O....O
    .O......
    .O.....O
    .OOOOOO.

:side-shooting gun = slide gun

:side-tracking See universal constructor.

:sidewalk (p1)

    .OO.OO
    ..O.O.
    .O..O.
    .O.O..
    OO.OO.

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

    ...........OO...
    ...OO.....O.O...
    ...O.O....O.....
    .....O...OO.O...
    ...O.OO.....OOO.
    .OOO.....O.O...O
    O...O.O.....OOO.
    .OOO.....OO.O...
    ...O.OO...O.....
    .....O....O.O...
    ...O.O.....OO...
    ...OO...........

: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:

    OO.........
    O..........
    .O..O......
    ...OO......
    ...O...O.OO
    ..O....OO.O
    ..OO.......

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.

    ..O...
    ..O.O.
    O....O
    OOOOOO
    ......
    ..OO..
    ..OO..

:sinking ship = canoe

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

    ...O...
    .OOO..O
    O...OOO
    OOO....
    ....OOO
    OOO...O
    O..OOO.
    ...O...

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

    .........O...........
    ........O.O..........
    .....................
    ......O...OO.........
    .....O.....O.........
    ......O.O............
    ........OO......O....
    ................O....
    ..O.....OO....OOO....
    ..O...........OO.....
    OOO.......OO..OO..OOO
    OO......O.OO....OOO..
    OO..OOO.O.O.....OOO..
    ..OOO................
    ..OOO......O.........
    ..........O.O........
    .....................
    ........O...OO.......
    .......O.....O.......
    ........O.O..........
    ..........OO.........

:skewed quad (p2)

    .OO....
    .O...OO
    ..O.O.O
    .......
    O.O.O..
    OO...O.
    ....OO.

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

    .............OO.........
    ............O..O........
    .............O.O........
    .........OO...O.........
    ..........O.OO..........
    ............O...........
    ............O...........
    ........................
    OO........OOO......O....
    OOOO.O........O...OO....
    O.O..OOO.O....O.........
    .........O....O.OOO..O.O
    ....OO...O........O.OOOO
    ....O......OOO........OO
    ........................
    ...........O............
    ...........O............
    ..........OO.O..........
    .........O...OO.........
    ........O.O.............
    ........O..O............
    .........OO.............

: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.)

    ..............OO.
    ..............OO.
    ........OOO......
    ..........O......
    .........O.....OO
    ..............O.O
    ................O
    .................
    .................
    .................
    .................
    .................
    .................
    .................
    .................
    .................
    .................
    .O...............
    .OO..............
    O.O..............

: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.

:slow glider construction Construction an object by a "slow salvo" of gliders all coming from the same direction, in such a way that timing of the gliders does not matter as long as they are not too close behind one another. This type of construction requires an initial seed object, such as a block, which is modified by each glider in turn until the desired object is produced.

In May 1997, Nick Gotts produced a slow glider construction of a block-laying switch engine from a block, using a slow salvo of 53 gliders. Constructions like this are important in the study of sparse Life, as they will occur naturally as gliders created in the first few generations collide with blonks and other debris.

Slow glider constructions are also useful in some designs for universal constructors. However, in this case the above definition is usually too restrictive, and it is desirable to allow constructions in which some gliders in the salvo are required to have a particular timing modulo 2 (a "p2 slow salvo"). This gives much greater flexibility, as blinkers can now be freely used in the intermediate construction steps.

:slow salvo See slow glider construction.

:small fish = LWSS

:small lake (p1) See also lake.

    ....O....
    ...O.O...
    ...O.O...
    .OO...OO.
    O.......O
    .OO...OO.
    ...O.O...
    ...O.O...
    ....O....

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

    OO.O.OO
    ...O...
    O.....O
    .OOOOO.
    .......
    .......
    OOO.OOO

: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.

    OO................OO
    .O................O.
    .O.O............O.O.
    ..OO............OO..
    .......O....O.......
    .....OO.OOOO.OO.....
    .......O....O.......
    ..OO............OO..
    .O.O............O.O.
    .O................O.
    OO................OO

The stabilizers make the domino spark largely inaccessible, but the snacker is extensible, as shown in the next diagram, and so a more accessible p9 domino spark can be obtained. In April 1998 Dean Hickerson found an alternative stabilizer that is less obtrusive than the original one, and this is also shown in this diagram.

    OO................................
    .O................................
    .O.O.........................OO...
    ..OO.......................O..O...
    .......O....O..............OOO....
    .....OO.OOOO.OO...O....O......OOO.
    .......O....O...OO.OOOO.OO...O...O
    ..OO..............O....O......OOO.
    .O.O.......................OOO....
    .O.........................O..O...
    OO...........................OO...

An end can also be stabilized by killer candlefrobras, although this isn't efficient.

: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.

    .O....................................
    .O....................................
    O.....................................
    .OOO.................OOO...OOO........
    .OO.O.........O...O.O......OOO........
    ..O...........OO.O.......O....OOOO....
    ......O......O...O.O...OO.O.....OO....
    ...O..O.OOO...OO.........O........OO.O
    ...OO.O.....O.....O.................O.
    .........O.OOOOOOO....................
    ......................................
    .........O.OOOOOOO....................
    ...OO.O.....O.....O.................O.
    ...O..O.OOO...OO.........O........OO.O
    ......O......O...O.O...OO.O.....OO....
    ..O...........OO.O.......O....OOOO....
    .OO.O.........O...O.O......OOO........
    .OOO.................OOO...OOO........
    O.....................................
    .O....................................
    .O....................................

:snake (p1)

    OO.O
    O.OO

: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)

    ....OO
    ....O.
    .....O
    ....OO
    OO.O..
    O.OO..

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

    ...OO.O..
    ...O.OO..
    OO.O.....
    .O..O.OOO
    O..O.O..O
    OOO.O..O.
    .....O.OO
    ..OO.O...
    ..O.OO...

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

    O.OO.OO
    OO.O.O.
    ......O
    OOO.OOO
    O......
    .O.O.OO
    OO.OO.O

and the p3 snake pit.

    .....OO....
    ....O..O...
    ....O.OO...
    .OO.O......
    O.O.O.OOOO.
    O.........O
    .OOOO.O.O.O
    ......O.OO.
    ...OO.O....
    ...O..O....
    ....OO.....

:snake siamese snake (p1)

    OO.OO.O
    O.OO.OO

: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.

    ...OO........OO...
    ...O.O......O.O...
    .....O......O.....
    ...O.OO....OO.O...
    .OOO..........OOO.
    O...O.O....O.O...O
    .OOO..........OOO.
    ...O.OO....OO.O...
    .....O......O.....
    ...O.O......O.O...
    ...OO........OO...

: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.

    ..................O........
    .................OOO.......
    ............OOO....OO......
    ...........O..OOO..O.OO....
    ..........O...O.O..O.O.....
    ..........O....O.O.O.O.OO..
    ............O....O.O...OO..
    OOOO.....O.O....O...O.OOO..
    O...OO.O.OOO.OO.........OO.
    O.....OO.....O.............
    .O..OO.O..O..O.OO..........
    .......O.O.O.O.O.O.....OOOO
    .O..OO.O..O..O..OO.O.OO...O
    O.....OO...O.O.O...OO.....O
    O...OO.O.OO..O..O..O.OO..O.
    OOOO.....O.O.O.O.O.O.......
    ..........OO.O..O..O.OO..O.
    .............O.....OO.....O
    .OO.........OO.OOO.O.OO...O
    ..OOO.O...O....O.O.....OOOO
    ..OO...O.O....O............
    ..OO.O.O.O.O....O..........
    .....O.O..O.O...O..........
    ....OO.O..OOO..O...........
    ......OO....OOO............
    .......OOO.................
    ........O..................

: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.

    ...........OO.....OOOO
    .........OO.OO...O...O
    .........OOOO........O
    ..........OO.....O..O.
    ......................
    ........O.............
    .......OO........OO...
    ......O.........O..O..
    .......OOOOO....O..O..
    ........OOOO...OO.OO..
    ...........O....OO....
    ......................
    ......................
    ......................
    ..................OOOO
    O..O.............O...O
    ....O................O
    O...O............O..O.
    .OOOO.................

: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 B29, big glider, brain, Canada goose, Coe ship, Cordership, crane, dart, dragon, ecologist, edge-repair spaceship, Enterprise, flotilla, fly, hammerhead, hivenudger, non-monotonic, Orion, puff suppressor, pushalong, quarter, Schick engine, seal, sidecar, snail, still life tagalong, sparky, swan, turtle, wasp, weekender and x66. See also Caterpillar.

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 twelve 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
    17c/45  orthogonal   Gabriel Nivasch et al.  Dec 2004
    c/6     diagonal     Nicolay Beluchenko      Sep 2005
    -----------------------------------------------------

A period p spaceship that 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>=2m+2n. (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 one of only two known c/5 diagonal spaceships. It was found by Jason Summers in January 2005.

    ..........OO..........
    .........O..O.........
    ........OO............
    .........O.OO.........
    ..........O.OOO.......
    ..........OO.OOO......
    ............O....OO...
    ............OOO....OO.
    ..O.........O.O.......
    .OOO........O..O......
    O...OO................
    O..O.O.......OO.O..O..
    .O.OO.OOOO...O...OOOO.
    ....OO.O...OO.......O.
    ....OO.OO..O.........O
    .....O...O........O.OO
    ...........O.......O..
    ......O.....O......O..
    ......O.....O..O......
    .......O...OO...OO....
    .......O....OO.O......
    ..............OO......

: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, particularly 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.

    OO....OO
    O.O..O.O
    ..O..O..
    O.O..O.O
    OO....OO

: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.

    ..........O....................
    ..........O...............OO...
    ......OO.O.OOO..........OO...O.
    O.OO.OO.OO..O.O...OO.OOOO......
    O...OO..O.OO..OOO..O.OO..OO...O
    O.OO....OOO.O.OOO......OO..O...
    ........OO.O...............O..O
    O.OO....OOO.O.OOO......OO..O...
    O...OO..O.OO..OOO..O.OO..OO...O
    O.OO.OO.OO..O.O...OO.OOOO......
    ......OO.O.OOO..........OO...O.
    ..........O...............OO...
    ..........O....................

: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.

    ..OO
    OOO.

: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.

    ......O...OOO.....OOO...O......
    ...OO.OOOOO.OO...OO.OOOOO.OO...
    .O.OO.O.....O.O.O.O.....O.OO.O.
    O...O.O...OOOOO.OOOOO...O.O...O
    ....OOO.....OO...OO.....OOO....
    .O..O.OOO.............OOO.O..O.
    ...O.......................O...

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

    OO....O
    .O..OOO
    .O.O...
    ..O.O..
    ...O.O.
    OOO..O.
    O....OO

: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.

    OO......
    ....OO..
    ..O....O
    ..O....O
    ....OO..
    OO......
    ...O..O.
    ...O..O.

: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.

    ..OO
    .OO.
    OO..

: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.radicaleye.com/DRH/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.

    .....O.....
    ....OOO....
    ..OOO.OOO..
    ..O.....O..
    .OO.....OO.
    OO.......OO
    .OO.....OO.
    ..O.....O..
    ..OOO.OOO..
    ....OOO....
    .....O.....

: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.

    ...O....
    ..O.O.OO
    ..O.OO.O
    OO......
    .O.O.OO.
    .O.O..O.
    ..O..O..
    ...OO...

: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.

    ......OO...........OO.
    ..O.O..O......OO.O..O.
    .O.OO.O.......O.OO.O..
    .O....OO...........OO.
    OO.OO.........O.OO...O
    ...OO.OO....OOO.OO.OO.
    OO....O....O.......O..
    .O.OO.O.....OOO.OO.O..
    O..O.O........O.O.O...
    OO....................

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.

    ..OO...............
    .OO.OO.............
    ..OOOO.............
    ...OO..............
    ...................
    ...OOOOO...........
    ..OOOOOOO..........
    .OO.OOOOO..........
    ..OO...............
    ...................
    ........O.O.....OO.
    ......O....O...O..O
    ......OO.....O.O..O
    .O..O..OOOO.O...OO.
    O.......OO.........
    O...O..............
    OOOO...............

: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) A p4 sparker which produces a 1-cell spark that is separated from the rest of the oscillator by two clear rows of cells. The first superfountain was found by Noam Elkies in February 1998. In January 2006 Nicolay Beluchenko found the much smaller one shown below. See also fountain.

    ...........O...........
    .......................
    .......................
    .....O..O.....O..O.....
    ...OO..O.OOOOO.O..OO...
    .....O...........O.....
    ...O.OO.........OO.O...
    .O.O...OOO...OOO...O.O.
    OOO.O.............O.OOO
    ..........O.O..........
    ....OOO...O.O...OOO....
    ....O..O...O...O..O....
    ...OOOO..O.O.O..OOOO...
    ...OO..OOO.O.OOO..OO...
    ..O...O...O.O...O...O..
    ...O..O.O.O.O.O.O..O...
    ....O.O.OO...OO.O.O....
    .....O...........O.....

: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.

    .OO..........................................................
    O..O...O...O...O...O...O...O...O...O...O...O...O...O...O...O.
    ....O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O
    O..O...O...O...O...O...O...O...O...O...O...O...O...O...O...O.
    .OOO.........................................................
    ..OO.........................................................
    ..OO.........................................................
    ...O.........................................................
    ...O.........................................................
    ...O.........................................................
    ...O.........................................................
    ...O.........................................................
    ...O.........................................................
    ...O.........................................................
    ..OO.........................................................
    ..OO.........................................................
    .OOO.........................................................
    O..O...O...O...O...O...O...O...O...O...O...O...O...O...O...O.
    ....O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O
    O..O...O...O...O...O...O...O...O...O...O...O...O...O...O...O.
    .OO..........................................................

: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.

    ...O....OO
    ...OOO..O.
    .OO...O.O.
    O..OO.O.OO
    .O......O.
    OO.O.OO..O
    .O.O...OO.
    .O..OOO...
    OO....O...

:swan (c/4 diagonally, p4) A diagonal spaceship producing some useful sparks. Found by Tim Coe in February 1996.

    .O..........OO..........
    OOOOO......OO...........
    O..OO........O.......OO.
    ..OO.O.....OO......OOO.O
    ...........OO...O.OO....
    .....O.O......OO........
    ..........OOO.O....O....
    .......OOO...O....O.....
    ........O.......O.......
    ........O......O........
    ........................
    ...........O............

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

    .O.O..
    O.....
    .O..O.
    ...OOO

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

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