Introduction | Bibliography

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:p = period

:p1 Period 1, i.e., stable. In the context of logic circuitry, this tends to mean that a mechanism is constructed from Herschel conduits that contain only still lifes as catalysts.

:p15 reflector A colour-changing glider reflector. Compare to the colour-preserving Snark. Minimum repeat time is 30 ticks.


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

:p1 megacell (p1 circuitry) A metacell constructed by Adam P. Goucher in 2008, capable of being programmed to emulate any Moore neighborhood rule, including isotropic and anisotropic non-totalistic rules. It fits in a 32768 by 32768 bounding box, with the resulting metacell grid at 45 degrees to the underlying Life grid. Like the OTCA metapixel, it includes a large "pixel" area so that the state of the megacell can easily be seen even at extremely small-scale zoom levels.

:p1 telegraph (p1 circuitry) A variant of Jason Summers' telegraph pattern, constructed in 2010 by Adam P. Goucher using only stable circuitry. A single incoming glider produces the entire ten-part composite lightspeed signal that restores the beehive-chain lightspeed wire to its original position. The signal is detected at the other end of the telegraph and converted back into a single output signal. This simplification came at the cost of a much slower transmission speed, one bit per 91080 ticks. In this mechanism, sending the entire ten-part signal constitutes a '1' bit, and not sending the signal means '0'.

:p30 shuttle = queen bee shuttle

:p45 glider gun A true-period glider gun discovered by Matthias Merzenich in April 2010. By most measures this is the smallest known odd-period gun of any type, either true-period or pseudo-period:


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

:p46 shuttle = twin bees shuttle

:p4 reflector The following glider reflector, discovered by Karel Suhajda in October 2012. Its minimum repeat time is 52 ticks. Unlike the pipsquirter-based reflectors it is a colour-preserving reflector, so it was made obsolete by the discovery of the much smaller stable Snark the following year.


................................O.........................
...............................O..........................
...............................OOO.......O.O..............
........................................O.OO..............
......................................OOO.....O...........
.....................................O...OOOOOOOO.........
..................................O.O.O..O.......O........
..............O...................OOOO.OO.OOOOOOO.O.......
..............OOO..................OOO.....O.O..O.O..OO...
.................O...................OOO.O.O...OO.O.O.O...
................OO.............OOO..OO.OOOOO....O.O.O.....
.............................O.O...OOO.OO.O..O.OOOO..O..OO
...........................OO.....O....O..O..O...O....O..O
...................O.......OO.O.O..O......O..O....OOOOOOO.
..................O...........O.O..O..O..O.........O......
..................OOO........O....O..O...........O...OO...
............................O.OOOOOOO........OO.O.OOO.O...
.............................O.........O.O....O.O.O.......
...................OO..........OOOOOOOOO.OOO..O.O.........
...................OO.......O...O.......O...O.O.O.........
...........................O..O...OOOO..O..O.O.O..........
.............................OO...O...O.O.O..O............
.............................O.....OOO.O.O.OO..O..........
........OO...............O...OOO.....O...O...OOO..........
...OO..O..O..................O...OO..O..O.OO..............
...O....O.O..................O...OOOO...O.O.OO............
OO.O.....O................OOO...O......OO...O.O...........
.O.O.OO....................OOO.....O..OO..O.O.O...........
O..O..O........OO...........OOO..OOO.OOO..O.O.OO..........
OO..O....O.....O.O..........O..O...O...O..O.O.............
.....OOOOO.......O...........O.O..O.OO...OOOO.............
................O..........O.O.O.OOO.OOO.O................
.......O.........OOO......O.OO.O..OO......................
......O.O..........O......O.....O......OO.O...............
.......O...................OOOOO......O..OO...............
.............................O........OO..................

: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

:p5 reflector A colour-changing glider reflector constructed by Noam Elkies in September 1998, by welding together two special-purpose period-5 sparkers. Compare to the colour-preserving Snark. Minimum repeat time is 25 ticks.


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

:p6 pipsquirter (p6) A pipsquirter oscillator found by Noam Elkies in November 1997, used in various hasslers and the colour-changing p6 reflector.


.....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.......

:p6 reflector (p7) A colour-changing glider reflector using the p6 pipsquirter. Compare to the colour-preserving Snark. Minimum repeat time is 24 ticks.


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

:p6 shuttle (p6) The following oscillator found by Nicolay Beluchenko in February 2004.


O.............
OOO...........
...O..........
..OO..........
..............
......O.......
.....OOOO.....
......O..O....
.......OOO....
..............
..........OO..
..........O...
...........OOO
.............O
This is extensible in more than one way:

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

:p72 quasi-shuttle (p72) The following oscillator, found by Jason Summers in August 2005. Although this looks at first sight like a shuttle, it isn't really.


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

:p7 pipsquirter A pipsquirter oscillator found by Noam Elkies in August 1999, used in various hasslers and the colour-changing p7 reflector.


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

A larger period-7 pipsquirter is used in cases where space is limited where the reflector should extend southward for as short a distance as possible:


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

:p7 reflector A colour-changing glider reflector using a p7 pipsquirter. Compare to the colour-preserving Snark. Minimum repeat time is 28 ticks. A high-clearance version is shown in p7 pipsquirter.


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

:p8 G-to-H A small periodic variant of a stable two-glider-to-Herschel component found by Paul Callahan in November 1998 and used in the Callahan G-to-H, Silver reflector and Silver G-to-H. Minimum repeat time is 192 ticks, though some lower periods such as 96 are possible via overclocking. Here a ghost Herschel marks the output signal location:


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

:p8 reflector A glider reflector constructed by Noam Elkies in September 1998, containing a figure-8, boat, eater, and block. Unlike the colour-preserving Snark, it is colour-changing. Minimum repeat time is 24 ticks.


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

:pair of bookends = bookends

:pair of tables = table on table

:paperclip (p1)


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

:parallel grey ship = with-the-grain grey ship

:Parallel HBK ((6,3)c/245912, p245912) A much smaller successor to the half-baked knightship, constructed by Chris Cain in September 2014. Several slow-salvo recipes are needed to support the multi-glider salvo seeds at the upstream end of the spaceship. "Parallel" means that these recipes are sent in parallel instead of one after the other, in series, as in the original HBK.

:Parallel HBK gun an armless constructor pattern that is programmed to build Parallel HBK oblique spaceships every 125906944 ticks. This gun was created by Chris Cain on 3 January 2015.

:parasite A self-sustaining reaction attached to the output of a rake or puffer, that damages or modifies the standard output. Compare tagalong. In 2009, while experimenting with novelty generating patterns in Golly, Mitchell Riley discovered parasites on glider streams from p20 and p8 backward rakes. In some cases, parasites can even "reproduce", as in the pattern below, though the number of copies is limited since they will eventually use up their host glider stream:


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

: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.

:parity Even or odd, particularly as applied to the phase of an oscillator or spaceship. For example, in slow salvo constructions, the intermediate targets are frequently period 2, most often because they contain blinkers or traffic lights. A glider striking a P2 constellation will generally produce a different result depending on its parity. Period-4 intermediate targets are rare (or not used), so it doesn't matter if an incoming glider is in phase 1 or phase 3 -- i.e., only the even/odd parity is important.

: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.

:period doubler See period multiplier.

:period multiplier A commonly used term for a pulse divider. Dividing the number of signals in a regular stream by N necessarily multiplies the period by N. For Herschel signals, a number of small period doubler, tripler, and quadrupler mechanisms are known. The term "period multiplier" can be somewhat misleading, because most such circuits can accept input streams that are not strictly periodic.

:perpendicular grey ship = against-the-grain grey ship

: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 = 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 that 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.


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

The following pattern demonstrates a p4 c/2 spaceship found by Jason Summers, in which the phase is changed as it deletes a forward glider. This phase change allows the spaceship to be used to delete a glider wave produced by a rake whose period is 2 (mod 4).


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

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.


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

:phi calculator (p1 circuitry) See pi calculator.

: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".


....O...
..O.O...
......O.
OO......
......OO
.O......
...O.O..
...O....
Every known phoenix oscillator has period 2. In January 2000, Stephen Silver showed that a period 3 oscillator cannot be a phoenix. The situation for higher periods is unknown.

:pi = pi-heptomino

:Pianola breeder A series of patterns by by Paul Tooke in 2010, based on a simplification and extension of the Gemini spaceship's construction mechanism. Tooke produced a number of slow-salvo-constructed patterns with superlinear growth, including a series of breeder patterns of previously unknown types. For some patterns, the Gemini's two construction arms were moved to a permanent stationary platform, using fourteen glider-loop channels instead of twelve.

Some of these breeder patterns remain difficult to classify unambiguously. For example, one pattern was designed to be an MSS breeder -- a modified Gemini spaceship puffing slide guns which build lines of blocks. However, the slide guns produce both moving and stationary objects at a linear rate, because streams of gliders are needed to reach out to the construction zone to do the push reaction and build more blocks. The pattern could therefore be classified as a hybrid MSM/MSS breeder. Other breeder patterns utilizing slide guns and universal constructor technology are likely to cause similar classification ambiguities.

:pi calculator (p1 circuitry) A device constructed by Adam P. Goucher in February 2010, which calculates the decimal digits of pi (the transcendental number, not the Life pattern!) and displays them in the Life universe as 8x10 dot matrix characters formed by arrangements of blocks along a diagonal stripe at the top. A push reaction moves a ten-block diagonal cursor to the next position as part of the "printing" operation for each new digit.

The actual calculation is done in binary, using a streaming spigot algorithm based on linear fractional transformations. The pi calculator is made up of a 188-state computer connected to a printing device via period-8 regulators and a binary-to-decimal conversion mechanism. The complete pattern can be found in Golly's Very Large Patterns online archive, along with the very similar 177-state phi calculator which uses a simpler algorithm to calculate and print the Golden Ratio.

:pi climber The reaction that defines rate of travel of the Caterpillar spaceship. A pi climber consists of a pi-heptomino "climbing" a chain of blinkers, moving 17 cells every 45 ticks, and leaving behind an identical chain of blinkers, shifted downward by 6 cells. A single pi climber does not produce any gliders or other output, but two or more of them traveling on nearby blinker chains can be arranged to emit gliders every 45 ticks. Compare Herschel-pair climber.


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

: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 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.


..............OO....OO....OO...............................
.............O..O.O....O.O..O..............................
.............OOO..........OOO..............................
................OO......OO.................................
...............O..OOOOOO..O................................
...............OO........OO................................
...........................................................
........O.............................OO..........O........
.......O...OOO......O.........O.......OO.........O.O.......
........O.OOOOO..........OOO...O...........................
............O...O.....O.OOOOO.O..................O.........
............OO....OOO.....O......................OO........
............OO....OOO....OO...................OOOOO........
...................O.....OO...................OO.OO.....OO.
.................................................O......O.O
.....................................................OO.O.O
.....................................................O.O.O.
.......................................................O...
...................................OOO.........O.O...O..O..
.......OO..........................O..O........O..O.....O..
.......OO..............................O.......O.O..O...O..
...................................O..O.............O...O..
...................................OOO..................O..
.....................................................O..O..
................................................O......O...
.............................................OO.OO...O.O.O.
.............................................OOOOO...OO.O.O
.........O......................................OO......O.O
........O.O.....................................O.......OO.
...........................................................
.OO.......O.....................................O.O........
O.O......OO......................................O.........
O.O.OO...OOOOO.............................................
.O.O.O...OO.OO.............................................
...O......O................................................
..O..O.....................................................
..O........................................................
..O...O....................................................
..O...O..O.O......................................OO.......
..O.....O..O......................................OO.......
..O..O...O.O...............................................
...O.......................................................
.O.O.O.....................................................
O.O.OO.....................................................
O.O......O.................................................
.OO.....OO.OO...................OO.....O...................
........OOOOO...................OO....OOO....OO............
........OO......................O.....OOO....OO............
.........O..................O.OOOOO.O.....O...O............
...........................O...OOO..........OOOOO.O........
.......O.O.........OO.......O.........O......OOO...O.......
........O..........OO.............................O........
...........................................................
................................OO........OO...............
................................O..OOOOOO..O...............
.................................OO......OO................
..............................OOO..........OOO.............
..............................O..O.O....O.O..O.............
...............................OO....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). See p6 pipsquirter, p7 pipsquirter.

: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

:pi wave A line of pi-heptominoes stabilizing one another. For example, an infinite line of pi-heptominoes arranged as shown below produces a pi wave that moves at a speed of 3c/10, and leaves no debris.


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

: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)


.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.

: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.


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.

See also PPS.

:pre-pulsar spaceship = PPS.

: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 originally constructed by Dean Hickerson in November 1991 that emits a stream of LWSSs representing the prime numbers. Some improvements were found by Jason Summers in October 2005.

:PRNG = pseudo-random number generator

: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 or equal to 14, with smaller periods being impossible. The first pseudo p14 gun was built by Dieter Leithner in 1995.

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-random glider generator A pseudo-random number generator in which the bits are represented by the presence or absence of gliders. 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-random number generator A pseudo-random number generator (PRNG) is an algorithm that produces a sequence of bits that looks random (but cannot really be random, being algorithmically determined).

In Life, the term refers to a PRNG implemented as a Life pattern, with the bits represented by the presence or absence of objects such as gliders or blocks. Such a PRNG usually contains gliders or other spaceships in a loop with a feedback mechanism that causes later spaceships to interfere with the generation of earlier spaceships. The period can be very high, as a loop of n spaceships has 2n possible states.

: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 and others have enumerated the pseudo still lifes up to 32 bits; these 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
25     7906676
26    20463274
27    52816265
28   136655095
29   353198379
30   914075620
31  2364815358
32  6123084116
--------------

: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. Hartmut Holzwart built the first c/4 diagonal puffer (as opposed to a wickstretcher) in February 2004.


.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).

:pufferfish (c/2, p12) A puffer discovered by Richard Schank in November 2014, from a symmetric soup search using an early version of apgsearch. It consists of a pair of B-heptominoes stabilised by a backend that leaves only pairs of blocks behind. It is simple enough to be easily synthesized with gliders.


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

:pufferfish spaceship (c/2, p36) Generally, any spaceship constructed using pufferfish. May refer specifically to the extensible c/2 spaceship constructed by Ivan Fomichev in December 2014, the first such spaceship to contain no period-2 or period-4 parts. (The first two or three rows might be considered to be period 2 or 4, but they are directly dependent on following rows for support.).

The pattern consists of two adjacent pufferfish spaceships, plus four copies of a nontrivial period 36 c/2 fuse for pufferfish exhaust, discovered using a randomized soup search.


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

: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.
In April 2006, Jason Summers found a way to make the classic puffer train into a p20 spaceship by adding a glider at the back:

OOO...........OOO.
O..O..........O..O
O......OOO....O...
O.....O..O....O...
.O.O..O...O....O.O
.......OOOO.......
.........O........
..................
..................
..................
.......OOO........
.......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 (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.


............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....................

:pull A reaction, most often mediated by gliders, that moves an object closer to the source of the reaction. See block pull, blinker pull, loaf pull; also elbow.

: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 Pixel Display (p30 circuitry) A large-scale raster line display device constructed by Mark Walsh in August 2010, where pulsars form the individual pixels in an otherwise empty grid. The published sample pattern displays and erases eight 7x5-pixel characters on each of two lines of text.

: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 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. For n=2, the simplest known stable pulse divider is the semi-Snark.

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 relatively small size and low period of this example made it useful for constructing compact glider guns of certain periods, but it became largely obsolete with the discovery of the semi-Snark. p7, p22, p36 and p46 versions of this pulse divider are also known.


.....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..

:push A reaction that moves an object farther away from the source of the reaction. See sliding block memory, pi calculator, elbow, universal constructor. See also pull, fire.

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

:python = long snake


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