A Selection of Life-like Rules
There are 218 = 262,144 possible Life-like rules, only a small fraction of which have been studied in any detail. In the descriptions below, all rules are specified in Golly/RLE format.
| Rule | Name | Description and sources |
|---|---|---|
| B1357/S1357 | Replicator | Edward Fredkin's replicating automaton: every pattern is eventually replaced by multiple copies of itself. |
| B2/S | Seeds | All patterns are phoenixes, meaning that every live cell immediately dies, and many patterns lead to explosive chaotic growth. However, some engineered patterns with complex behavior are known. |
| B25/S4 | This rule supports a small self-replicating pattern which, when combined with a small glider pattern, causes the glider to bounce back and forth in a pseudorandom walk. | |
| B3/S012345678 | Life without Death | Also known as Inkspot or Flakes. Cells that become alive never die. It combines chaotic growth with more structured ladder-like patterns that can be used to simulate arbitrary Boolean circuits. |
| B3/S23 | Life | Highly complex behavior. |
| B34/S34 | 34 Life | Was initially thought to be a stable alternative to Life, until computer simulation found that larger patterns tend to explode. Has many small oscillators and spaceships. |
| B35678/S5678 | Diamoeba | Forms large diamonds with chaotically fluctuating boundaries. First studied by Dean Hickerson, who in 1993 offered a $50 prize to find a pattern that fills space with live cells; the prize was won in 1999 by David Bell. |
| B36/S125 | 2x2 | If a pattern is composed of 2x2 blocks, it will continue to evolve in the same form; grouping these blocks into larger powers of two leads to the same behavior, but slower. Has complex oscillators of high periods as well as a small glider. |
| B36/S23 | HighLife | Similar to Life but with a small self-replicating pattern. |
| B3678/S34678 | Day & Night | Symmetric under on-off reversal. Has engineered patterns with highly complex behavior. |
| B368/S245 | Morley | Named after Stephen Morley; also called Move. Supports very high-period and slow spaceships. |
Several more rules are listed and described in the MCell rule list and by Eppstein (2010), including some rules with B0 in which the background of the field of cells alternates between live and dead at each step.
Any automaton of the above form that contains the element B1 (e.g. B17/S78, or B145/S34) will always be explosive for any finite pattern: at any step, consider the cell (x,y) that has minimum x-coordinate among cells that are on, and among such cells the one with minimum y-coordinate. Then the cell (x-1,y-1) must have exactly one neighbor, and will become on in the next step. Similarly, the pattern must grow at each step in each of the four diagonal directions. Thus, any nonempty starting pattern leads to explosive growth.
Read more about this topic: Life-like Cellular Automaton
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