OCA:Brian's Brain

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Brian's Brain
x=0, y = 0, rule =/2/3 ! #C [[ THEME Generations ]] #C [[ RANDOMIZE2 THUMBLAUNCH OFF THUMBNAIL THUMBSIZE 2 GRID ZOOM 4 WIDTH 500 HEIGHT 500 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]]
LifeViewer-generated soup (refreshes with page)
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".

On November 12, 2020, Yoel Matveyev published a Rule 110 unit cell for Brian's Brain, proving the rule Turing-complete [1]. The unit's design follows the model of the Rule 110 unit cell constructed by Matveyev for his rule Fireworld and does not contain XOR gates. Instead, it uses AND-NOT gates and toggle flip-flops.

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[2]. 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.

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[3], 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.[1] 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

Wire2 is a variant of Brian's Brain running inside wires. It is invented by Blah. Wilfred is a variant of Brian's Brain with an additional indestructible state. It is invented by Brian Prentice. Wire3 is another variant of Brian's Brain with an additional indestructible state, inspired by Wilfred and Fireworld2. It is invented by Yoel Matveyev.

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 indestructible state-3 neighbors.

Patterns

All oscillators, spaceships and any other patterns of Brian's Brain also works in Wire2, Wilfred and Wire3.

Wire2 runs Brian Brain patterns inside the 3-state wires. Each wire cell may be empty, contain a live cell or a State 3 cell, much like electrons and electron tails in WireWorld. Patterns running inside an infinite 2D wire in Wire2 would evolve completely identically to plain Brian's Brain.

Due to the additional indestructible state, Wilfred also features a wire that can carry signals. Unlike Wire2, signals run on the wires' surface. Thus. Wilfred without any wires is completely identical to Brian's Brain. (citation needed)

Wire3, inspired by Wilfred, uses the same concept, but has different wire interaction rules based on Fireworld2, which make logic construction very easy. Like Wilfred, Wire3 without any wires is identical to Brian's Brain [6].

References

  1. 1.0 1.1 Yoel Matveyev (November 15, 2020). Re: Turing - complete Generations rules (discussion thread) at the ConwayLife.com forums
  2. praosylen (April 16, 2020). Re: Brian's Brain (discussion thread) at the ConwayLife.com forums
  3. FWKnightship (May 12, 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 Matveyev (November 9, 2020). Re: Wilfred (discussion thread) at the ConwayLife.com forums
  6. Yoel Matveyev (December 29, 2020). Re: Wire3 (discussion thread) at the ConwayLife.com forums

External links