OCA:Move

Move
x=64, y = 64, rule = B368/S245 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 RANDSEED 1729 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]] LifeViewer-generated pseudorandom soup
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Rulestring	245/368 B368/S245
Rule integer	26952
Character	Stable
Black/white reversal	B012578/S134678

Move (or Morley) 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" sqrt replicator rule 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.

On August 20, 2020, Layz Boi constructed a Rule 110 unit cell in Move, proving the rule Turing-complete.

Notable patterns

The move rule contains a large variety of known patterns, including many guns, spaceships, and puffers.

Still lifes

Below is an enumeration of small still lifes in the move rule. 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.

Size Count ≤ 3 0 4 1 5 1 6 2 7 2 8 4 9 1 10 3

x = 23, y = 39, rule = B368/S245 bo$obo$bo3$o$3o$2bo3$2o5b2o$o2bo2bo2bo$2b2o3b2o3$o6b2o$3o3bo2bo$2bo3bo bo$2b2o3bo3$obo4b2o4b2o6bo$2obo2bo2bo2bo2bo3b3o$2bo3bo2bo3bo2bo3b3o$2b 2o3b2o5b2o4bo3$o$3o$2bo$2b3o$4bo3$2o4b2o5b2o$bo5bo6bo$4o2b2ob2o3b3o$2b o6bo3b3o$2b2o5b2o4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] Some small still lifes in Move (click above to open LifeViewer) RLE: here Plaintext: here

Common objects

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.

Rank	Object	Name	Period	Relative Frequency
1	Blinker		2	0.305
2	xp4_37		4	0.155
3	Tub		1	0.128
4	xp2_f		2	0.108
5	xp4_165		4	0.078
6	xp2_272		2	0.058
7	xp2_ff		2	0.056
8	Z-pentomino		1	0.047
9	xp4_163		4	0.025
10	xs8_32da		1	0.014

Spaceships

There are spaceships known of twenty different speeds (where those in bold have occurred naturally, and those in italics seminaturally);

• orthogonal: c/2(, 2c/4, 3c/6, 4c/8, 10c/20, 26c/52), 3c/7, 2c/5, c/3(, 2c/6), 2c/7, c/4, c/5, 4c/23, c/6, c/7, c/10, 11c/120, 13c/170
• diagonal: c/3, c/4, c/5, c/6, c/7
• knightwise: (2,1)c/5, (2,1)c/6

Of these, by far the most well-known is the jellyfish, which travels at c/7 diagonally.

x = 810, y = 173, rule = B368/S245 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#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 3 WIDTH 2480 HEIGHT 540 ]]

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. 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, who also found a four-engine breeder, the first pattern with quadratic growth.

There also a 11c/120 rephasing 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.

x = 4, y = 4, rule = B368/S245 bo$obo$3bo$2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 3 ZOOM 48 GPS 3 AUTOSTART TRACKLOOP 7 1/7 -1/7 ]]

The jellyfish (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 2, y = 6, rule = B368/S245 o$bo$bo$bo$bo$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 3 ZOOM 48 GPS 3 ]]

A 6-cell predecessor of a common puffer (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 92, y = 42, rule = B368/S245 15b2o$14b4obo$11b2obo2b2ob2o$10bo3b3o4b2o18b4o$9bo2bobo2b2o3bo18b4o$4o 5bo2bobo2b2o3bo$4o6bo3b3o4b2o$11b2obo2b2ob2o$14b4obo33bo$15b2o37bo$51b ob3o$51bo2bo13b4o3bo$40b2o10bobo13b3o3b2o$24b2o14b3o9b3o11b3obob3o$24b 2o14b3o8bo2bo11b3obo3b2o$24b2o14b2o8bobo12b4o4bo$24b2o26bo13b3obo3b2o$ 52bo13b3obob3o$50b5o13b3o3b2o$51bo3b2o11b4o3bo$50bo5bo$20b2o28bo2b2obo $16b3ob4o26b3o$17bobo3bo26b2obo$17b2o4b2o26bobobobo$16b2o4b3o28bo3bo8b 2o$18bo3b3o16b2o9b2ob2obo7b2o$16b2o4b3o16b3o6bob3ob2o8b2o$17b2o4b2o16b 3o8b4o10b2o$17bobo3bo17b2o11bo$16b3ob4o$20b2o$62b2o$61b4obo$58b2obo2b 2ob2o$57bo3b3o4b2o18b4o$56bo2bobo2b2o3bo18b4o$47b4o5bo2bobo2b2o3bo$47b 4o6bo3b3o4b2o$58b2obo2b2ob2o$61b4obo$62b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ MAXGRIDSIZE 9 HEIGHT 420 WIDTH 900 THUMBSIZE 2 ZOOM 8 GPS 30 AUTOSTART LOOP 404 ]]

Jason's bow, a period-404 double-barreled gun (click above to open LifeViewer) RLE: here Plaintext: here

External links

• Move at Adam P. Goucher's Catagolue
• Move at David Eppstein's Glider Database
• Move/Morley (245/368) (discussion thread) at the ConwayLife.com forums
• MCell built-in Life rules: Move at Mirek Wójtowicz's Cellebration page