OCA:Brian's Brain

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Brian's Brain
Brian's Brain rule
Rulestring /2/3
B2/S/C3
B2/S/G3
Character Chaotic

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".

Patterns

x = 4, y = 4, rule = /2/3 2.A$A2B$.2BA$.A! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Generations AUTOSTART GPS 3 THUMBSIZE 4 ]]
A period-3 oscillator
(click above to open LifeViewer)
RLE: here Plaintext: here

Usually, a random starting configuration in Brian's Brain will explode, emitting many spaceships, rakes, breeders, puffers and wavestretchers.

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. Period-4 oscillators are also known to exist[1]. Larger period oscillators with periods dividable by 3 can be constructed by gun reactions. 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[2], as well as gun constructions shooting various other spaceships and rakes at different periods. Brian's Brain is Turing complete, as demonstrated by an infinitely extendable tiling of Rule 110 units.[3] 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.[4]

A collection of patterns in this rule can be found in Mirek's Cellebration.

Variants

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Wilfred is a variant of Brian's Brain with an additional indestructable state. It is invented by Brian Prentice.

Rules

According to the Rule table[5], cells behave as follows:

A state-1 cell is born if:

  • It touches exactly 2 state-1 neighbors. (The same as Brian's Brain)
  • OR It touches exactly 1 state-1 neighbor and exactly 3 indestructable state-3 neighbors.

Patterns

All oscillators and spaceships in Brian's Brain also works in Wilfred. Due to the additional indestructable state, Wilfred also features a wire that can carry signals. (citation needed)

References

  1. A for awesome (Apr 16, 2020). Re: Brian's Brain (discussion thread) at the ConwayLife.com forums
  2. FWKnightship (May 12, 2020). Re: Turing - complete Generations rules (discussion thread) at the ConwayLife.com forums
  3. Yoel (Nov 15, 2020). Re: Turing - complete Generations rules (discussion thread) at the ConwayLife.com forums
  4. Rocknlol (December 31, 2020). Re: Brian's Brain (discussion thread) at the ConwayLife.com forums
  5. Yoel (November 9, 2020). Re: Wilfred (discussion thread) at the ConwayLife.com forums

External links