OCA:Move

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Move
Move rule
Rulestring 245/368
B368/S245
Rule integer 26952
Character Stable
Black/white reversal B012578/S134678

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. 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.

Notable patterns

The move rule contains a large variety of known patterns, including many guns, spaceships[1], 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.

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
Blinker.png
2 0.305
2 xp4_37
Move2.GIF
4 0.155
3 Tub
Tub.png
1 0.128
4 xp2_f
Move4.GIF
2 0.108
5 xp4_165
Move5.GIF
4 0.078
6 xp2_272
Move6.GIF
2 0.058
7 xp2_ff
Move7.GIF
2 0.056
8 Z-pentomino
Move8.GIF
1 0.047
9 xp4_163
Move9.GIF
4 0.025
10 xs8_32da
Move10.GIF
1 0.014

Spaceships

There are at least 16 spaceships known in the move rule.[1] Of these, by far the most well-known is the jellyfish, which travels at speed c/7 diagonally.

Guns

At least 11 guns have been found, most of them by Stephen Morley and Jason Summers.[2] 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.

x = 4, y = 4, rule = B368/S245 bo$obo$3bo$2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ AUTOSTART GPS 3 TRACKLOOP 7 1/7 -1/7 ]]
The jellyfish
(click above to open LifeViewer)
RLE: here Plaintext: 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$62b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
Jason's bow, a period 404 double-barreled gun
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 2, y = 6, rule = B368/S245 o$bo$bo$bo$bo$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
A 6-cell predecessor of a common puffer
(click above to open LifeViewer)
RLE: here Plaintext: here

Notes

  1. The name given to this rule in Golly, in reference to Stephen Morley, who has extensively studied it.
  2. Computed using the EnumStillLifes.c script located here.

References

  1. 1.0 1.1 "Move (B368/S245)". David Eppstein. Retrieved on March 28, 2009.
  2. "b368s245 Guns". Stephen Morley. Retrieved on March 28, 2009.

External links