: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.
OO.........................OO .O.........................O. .O.O.......O.............O.O. ..OO.....O..O.....O......OO.. ............O.....OO......... ........O..........OO........ ........O...OO....OO......... .........OOOOO............... ............................. .........OOOOO............... ........O...OO....OO......... ........O..........OO........ ............O.....OO......... ..OO.....O..O.....O......OO.. .O.O.......O.............O.O. .O.........................O. OO.........................OO
:pair of bookends = bookends
:pair of tables = table on table
..OO. .O..O .O.OO OO.O. O..O. .OO..
: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)
.....O..... ....O.O.... .O..OO..... .OOO....... .....OOO... ...OO...O.. ..O....O..O .O.O.O.O.OO .O.O...O.O. OO.O.O.O.O. O..O....O.. ..O...OO... ...OOO..... .......OOO. .....OO..O. ....O.O.... .....O.....
:penny lane (p4) Found by Dave Buckingham, 1972.
...OO.....OO... ...O.......O... OO.O.......O.OO OO.O.OOOOO.O.OO ....O..O..O.... .....OOOOO..... ............... .......O....... ......O.O...... .......O.......
: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.
..O....O.. OO.OOOO.OO ..O....O..The pentadecathlon is the only known oscillator which is a polyomino in more than one phase.
:pentant (p5) Found by Dave Buckingham, July 1976.
OO........ .O........ .O.O...... ..OO....OO .........O .....OOOO. .....O.... ..O...OOO. ..OOOO..O. .....O.... ....O..... ....OO....
:pentaplet Any 5-cell polyplet.
:pentapole (p2) The barberpole of length 5.
OO...... O.O..... ........ ..O.O... ........ ....O.O. .......O ......OO
: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.)
...........OO ...........O. .........O.O. .........OO.. .....OO...... ......O...... ......O...... ......OO..... ..OO......... .O.O......... .O........... OO...........
: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.
:phi The following common spark. The name comes from the shape in the generation after the one shown here.
.OOO. O...O O...O .OOO.
:phoenix Any pattern all of whose cells die in every generation, but which never dies as a whole. In fact it can be proved that a spaceship cannot be a phoenix, so the term applies mainly to oscillators, of which the following (found by the MIT group in December 1971) is the smallest known (and is sometimes simply called "the phoenix").
....O... ..O.O... ......O. OO...... ......OO .O...... ...O.O.. ...O....
: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.
OOO O.O O.O
:pincers = great on-off
:pinwheel (p4) Found by Simon Norton, April 1970. Compare clock II.
......OO.... ......OO.... ............ ....OOOO.... OO.O....O... OO.O..O.O... ...O...OO.OO ...O.O..O.OO ....OOOO.... ............ ....OO...... ....OO......
:pi portraitor (p32) Found by Robert Wainwright in 1984 or 1985. Compare with gourmet and popover.
...........OO........... ......OO.O....O.OO...... ......O..........O...... .......OO......OO....... ....OOO..OOOOOO..OOO.... ....O..O........O..O.... .OO.O.O..........O.O.OO. .O.O.O............O.O.O. ...O................O... .O..O..............O..O. ....O.......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. .OO.O.O..........O.O.OO. ....O..O........O..O.... ....OOO..OOOOOO..OOO.... .......OO......OO....... ......O..........O...... ......OO.O....O.OO...... ...........OO...........
: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.
.....O......... .....O......... ............... ...O...O....... .OOO.O.OOO..... O...OO....O.... O.OO..OO.O.O... .O..OO..OO.O... ..OO..OO.O.O.OO ....O..O.O.O.OO ....OOOO.OO.... ........O...... ......O.O...... ......OO.......
:pi ship A growing spaceship in which the back part consists of a pi-heptomino travelling at a speed of 3c/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.
............O............ ...........O.O........... OO........OO.OO........OO OO.....................OO
:piston (p2) Found in 1971.
OO.......OO O.O..O..O.O ..OOOO..O.. O.O..O..O.O OO.......OO
: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.
.OO. O..O O..O .OO.
:pond on pond (p1) This term is often used to mean bi-pond, but may also be used of the following pseudo still life.
.OO...OO. O..O.O..O O..O.O..O .OO...OO.
:popover (p32) Found by Robert Wainwright in August 1984. Compare with gourmet and pi portraitor.
.....................O.......... .....................O.......... .....................OOO........ .............OO.......OO........ .............OO..OOO..OO........ ...................OOO.......... ...................OOO.......... ..............OO................ ..OOO........O..O............... ..OOO........O.O................ OOO..OO...O...O....OOO.......... .....OO...O..................... ....OOO...O..................... ....O.................OO...OO... ....O...........OOO..O..O..OO... ........O.......O.O...O.O....... .......O.O......O.O....O........ ...OO..O..O................O.... ...OO...OO.................O.... .....................O...OOO.... .....................O...OO..... ..........OOO........O...OO..OOO .................OO........OOO.. ................O..O.......OOO.. ................O.O............. ..........OOO....O.............. ..........OOO................... ........OO..OOO..OO............. ........OO.......OO............. ........OOO..................... ..........O..................... ..........O.....................
:population The number of ON cells.
:P-pentomino Conway's name for the following pentomino, a common spark.
OO OO O.
:pre-beehive The following common parent of the beehive.
OOO OOO
:pre-block The following common parent of the block. Another such pattern is the grin.
O. OO
: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.)
OOO...OOO O.O...O.O OOO...OOO
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.
In late 1997 Noam Elkies found that a pre-pulsar can also act as a tagalong pulled by a pair of Tim Coe's large p5 c/5 spaceships, thereby giving a p15 c/5 spaceship. In May 1998 David Bell found that it could also be pulled by spiders, giving a p30 c/5 spaceship (due to a period-doubling effect). This spaceship, and a variant noticed by Alan Hensel, has been very useful in creating new c/5 puffers.
:pressure cooker (p3) Found by the MIT group in September 1971. Compare mini pressure cooker.
.....O..... ....O.O.... ....O.O.... ...OO.OO... O.O.....O.O OO.O.O.O.OO ...O...O... ...O...O... ....OOO.... ........... ...O.OO.... ...OO.O....
:primer A pattern constructed by Dean Hickerson in November 1991 that emits a stream LWSSs representing the prime numbers.
:protein (p3) Found by Dave Buckingham, November 1972.
....OO....... ....O........ ......O...... ..OOOO.O.OO.. .O.....O.O..O .O..OO.O.O.OO OO.O.....O... ...O..OO.O... ...O....O.... ....OOOO..... ............. ....OO....... ....OO.......
: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 13. (Gliders cannot travel in a stream of period 13 or less, so this result is the best possible.) 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.
..........OO ...........O .........O.. .......O.O.. ............ .....O.O.... ............ ...O.O...... ............ ..OO........ O........... OO..........
: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 2c/5 orthogonal puffer in February 1999.
.OOO......O.....O......OOO. O..O.....OOO...OOO.....O..O ...O....OO.O...O.OO....O... ...O...................O... ...O..O.............O..O... ...O..OO...........OO..O... ..O...OO...........OO...O..
: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.)
.OOO...........OOO O..O..........O..O ...O....OOO......O ...O....O..O.....O ..O....O........O.
:puff suppressor An attachment at the back of a line puffer that suppresses all or some of its puffing action. The example below 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.
............O.................... ..........OO.O................... ..........OO...O................. ........O...OO.O.....O........... ........OOOO.OO...OOOO.......O.O. ......O......O....OOO.....O.O..O. ......OOOOOOO...O...O....O..O.... ...O.O......OO..O...O.O.OO....O.. ..OOOOOOOOO.....O..OO........O... .OO..............O.OO.OOOO...O..O OO....OO.O..........O...O..O.O... .OO....O........OOO......O.O.O..O .........O......OO......O....OO.. .OO....O........OOO......O.O.O..O OO....OO.O..........O...O..O.O... .OO..............O.OO.OOOO...O..O ..OOOOOOOOO.....O..OO........O... ...O.O......OO..O...O.O.OO....O.. ......OOOOOOO...O...O....O..O.... ......O......O....OOO.....O.O..O. ........OOOO.OO...OOOO.......O.O. ........O...OO.O.....O........... ..........OO...O................. ..........OO.O................... ............O....................
: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.
..OOO...OOO.. ............. O....O.O....O O....O.O....O O....O.O....O ..OOO...OOO.. ............. ..OOO...OOO.. O....O.O....O O....O.O....O O....O.O....O ............. ..OOO...OOO..
: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.
.....O.. ...OOO.. ..O...OO O..O..O. O...O.O. O....O.. ........ ..OOO...
:pulse = 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.
.....OO................... .....OO................... .......................... ..................OO...... .................O..O..... .................O.O..O..O O...............OO.O.OOOOO .OO...........O...OO...... OO...............OO..OOO.. .............O...O.O..O.O. ........OO.......OO..OO.O. ........OO....O...OO...O.. ................OO.O.OO... .................O.O.O.... .................O.O..O... ..................O..OO... ..OO...................... ...O...................... OOO....................... O......................... .......................... ............OO............ ............O............. .............OOO.......... ...............O..........
:pulshuttle V (p30) Found by Robert Wainwright, May 1985. Compare Eureka.
.............O..............O............. ............O.O.......O....O.O............ .............O......OO.OO...O............. ......................O................... ..OO......OO..................OO......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 ..OO......OO........OO.OO.....OO......OO.. ......................O................... .......................................... .......................................... ..OO......OO..................OO......OO.. O....O..O....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 ..OO......OO..................OO......OO.. .......................................... .......................................... ......................O................... ..OO......OO........OO.OO.....OO......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 ..OO......OO..................OO......OO.. ......................O................... .............O......OO.OO...O............. ............O.O.......O....O.O............ .............O..............O.............
: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:
..O............ ..O............ OOO............ ............... ......OOO...... .......O....... ............OOO ............O.. ............O..
: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.
..OOO.O..... .OOOO.O..... OO.......... .O.O........ ..OOOO.O.... ...OOO...... ............ ............ ......OOOOO. ......O....O ......O..... .......O...O .........O..
:pyrotechnecium (p8) Found by Dave Buckingham in 1972.
.......O........ .....OOOOO...... ....O.....O..... .O..O.O.OO.O.... O.O.O.O....O..O. .O..O....O.O.O.O ....O.OO.O.O..O. .....O.....O.... ......OOOOO..... ........O.......
:pyrotechneczum A mistaken spelling of pyrotechnecium, caused by an early transcription error.
:python = long snake