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Brian's Brain (also called BB, or simply Brain) is a cellular automaton and one of the best-known Generations rules. It is similar to Seeds, but with an additional state; dead cells get born if they have exactly two live neighbors, and live cells never survive, but instead of dying immediately, they advance to a third state, not considered "live" for the purpose of cell birth, before dying. The rule was first considered by Brian Silverman in the mid-1990s.
Brian's Brain can be thought of as emulating a neural network, with state 0 representing "ready", state 1 representing "firing", and state 2 representing "refractory"; the rule can then be stated as "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".
The first oscillators were discovered by Michael Sweney in December 1999. No period-2 oscillators exist (as in any Generations rule with more than two states); an example of a period-3 oscillator is shown to the left. Some periodic agars and wicks have also been constructed in Brian's Brain.
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.
A collection of patterns in this rule can be found in Mirek's Cellebration.
- FWKnightship (May 12, 2020). Re: Turing - complete Generations rules (discussion thread) at the ConwayLife.com forums