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Move (or Morley[note 1]) is a Life-like cellular automaton in which cells survive from one generation to the next if they have 2, 4, or 5 neighbours. Cells are born if they have 3, 6, or 8 neighbours, and differs from the "nearby" B36/S245 in the presence of birth on 8 alive neighbours. Random starting patterns tend to stabilize into ash consisting of small still lifes and period 2 and 4 oscillators. It also contains one commonly-occurring slow-moving spaceship and slow-moving puffer. The time required to stabilize is generally much shorter than in the Game of Life.
The move rule contains a large variety of known patterns, including many guns, spaceships[2], and puffers.
Still lifes
Below is an enumeration of small still lifes in the move rule.[note 2] Despite the abundance of interesting moving patterns in this rule, there are relatively few still lifes. It can be seen that there are still lifes of arbitrarily large size by noting that for every odd number of cells greater than 5, there is an obvious extension of the Z-pentomino for that number of cells that is a still life. Also, every lake is a still life, so for any n ≥ 3, there is at least one still life with 8n cells.
Random starting patterns tend to stabilize into a much lower density (around 0.4%) than in Game of Life (around 3%). There are many more oscillators than still lifes in Move. About five sixths of objects in random settled areas are oscillators.
There are spaceships known of seventeen different speeds;[3] c/2(, 2c/4, 10c/20, 26c/52), 2c/5, c/3(, 2c/6), 2c/7,[4] c/4, c/5, 4c/23, c/6, c/7, c/10, 11c/120, 13c/170, (2,1)c/5, (1,1)c/3, (1,1)c/4, (1,1)c/5, (1,1)c/6 and (1,1)c/7. Of these, by far the most well-known is the jellyfish, which travels at speed c/7 diagonally. On December 18, 2020, AforAmpere found the first known knightship in this rule, specifically a (2,1)c/5.[5]
Spaceships of known speeds (click above to open LifeViewer)
Guns
At least 11 guns have been found, most of them by Stephen Morley and Jason Summers.[6] The first gun to be constructed was called Safalra's bow and was discovered on September 21, 2002 by Stephen Morley. It shoots two c/7 diagonal spaceships in opposite directions every 404 generations. Jason's bow, shown to the right, is a smaller version of Safalra's bow that was found by Jason Summers.
Other patterns
One puffer that commonly appears from random starting configurations is shown below. Its period is 170 and it travels at speed 13c/170. It is formed by a common six-cell pattern, which is the smallest pattern that exhibits infinite growth in this rule. (Compare this with ten cells for infinite growth in Life.) In B36/S245 (the sqrt replicator rule), it becomes the rule's namesake Θ(√t) replicator.
After being discovered by Alan Hensel in 1993, it was first corderised by Dean Hickerson in 1998, then reduced by Stephen Morley and David Eppstein in 2002, and again to its present four-engine state (excluding an ephemeral perpendicular instance) in 2021 by 4.66920 16091,[7] who also found a four-engine breeder, the first pattern with quadratic growth.[8]
There also a 11c/120 'overclocking' of this puffer, caused by an interaction with a temporary blinker in between, in a spaceship that first occurred naturally in a soup found by Ian07 on November 25, 2018.[9]
