List of Generations rules: Difference between revisions
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Revision as of 18:55, 21 December 2025
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| Brian's Brain | |
| Rulestring | /2/3 B2/S/C3 B2/S/G3 |
|---|---|
| Character | Chaotic |
Also called BB, or simply Brain, this is unquestionably one of the best known and most intresting CA rules. If we name the possible cell values based on a simplistic neural analogy, viz. 0 = "ready", 1 = "firing", 2 = "refractory", then this simple rule can be stated thusly: Only a cell in the ready state may fire and it will only do so if exactly 2 of its neighbors are firing. After firing for one step, a cell spends a step in the refractory state before regaining readiness. Many principles of seeds can also be applied to this rule.
Although the rule is relatively old, it has never been systematically explored. The rule is so lively that it's not easy to construct stable patterns in it. In December 1999, Michael Sweney discovered the first oscillators in this rule. A group of lasers shooting the smallest photon were discovered by Giles Edkins no later than May 2001, based on which signal reflectors, duplicator, AND gate, OR gate and XOR gate have been explicitly constructed, as well as gun constructions shooting various other spaceships and rakes at different periods. Larger period oscillators with periods divisible by 3 can be constructed by gun reactions. Some periodic agars and wicks have also been constructed in Brian's Brain. Brian's Brain is Turing complete, as demonstrated by an infinitely extendable tiling of Rule 110 units. The tiling also demonstrates a usage of gun period doublers, flip-flops, arbitrary length memory units and custom spaceship flotilla generators used for Rule 110's output display.
On December 31, 2020, Rocknlol found a c/5 orthogonal spaceship in Brian's Brain - the first orthogonal non-light-speed spaceship in this rule.
| Brain 6 | |
| Rulestring | 6/246/3 B246/S6/C3 B246/S6/G3 |
|---|---|
| Character | Chaotic |
An interesting variation of the immortal Brian's Brain, with many patterns constructed. Dead cells get born if they have two, four or six live neighbors, and live cells survive only if it has exactly six live neighbors, and similar to Brain's Brain, live cells advance to a third state, not considered "live" for the purpose of cell birth, before dying.
| Frogs | |
| View static image | |
| View animated image | |
| Rulestring | 12/34/3 B34/S12/C3 B34/S12/G3 |
|---|---|
| Character | Chaotic |
A rule named after its very common frog-like gliders.
| A predecessor for a common constellation (click above to open LifeViewer) |