Brian's Brain
B2/S/3 — three states, and a compulsory rest after firing
Three states — ready, firing, recovering. A cell that fires must rest before it can fire again, so activity travels forwards and never doubles back.
How it works
In plain English, before the notation
Each cell is in one of three states: ready, firing, or recovering. A ready cell fires when exactly two of its neighbours are firing. A firing cell always stops and enters recovery — it has no choice. A recovering cell always returns to ready. Because a cell cannot fire again immediately, activity cannot spread backwards into the region it just came from, so everything travels in a single direction.
Watch waves that cannot back up
- Open Presets and load "Brian’s Brain", then press Play.
- Follow a single travelling packet. The bright head is firing; the dimmer trail behind it is recovering.
- Pause, select the "Refractory" paint state in the dock, and draw a wall. Incoming packets cannot pass through it while it is recovering.
Starting configurations
Loads straight into the simulatorTry any rule
The catalogue covers a few dozen rules. Here you can run any of the 262,144 two-state grid rules, or any of the 256 one-dimensional rules, including ones nobody has written up.
Well-known rules
Where it came from
Devised by Brian Silverman in the early 1980s. It is the best-known member of the Generations family, in which a cell that stops firing must pass through one or more cooling states before it can fire again — the same idea as a refractory period in an excitable medium.
The rule, precisely
What each cell looks at
The 8 cells touching it, including diagonals (the Moore neighbourhood)
What a cell can be
Three states: 0 = ready, 1 = firing, 2 = recovering
The update
if state = 0 and (firing neighbours) = 2 then 1; if state = 1 then 2; if state = 2 then 0
B2/S/3 in Generations notation: Birth on 2 firing neighbours, an empty Survival set (a firing cell never stays firing), and 3 states in total.
Directional activity, and almost nothing that stays put
The forced recovery state changes the character of the rule completely compared with a two-state rule:
- Nearly all patterns produce packets of firing cells that travel in a straight line with a fading tail.
- Two packets meeting head-on annihilate: each runs into the other’s recovering trail and has nowhere to go.
- Closed loops of activity can circulate indefinitely, chasing their own tail around the loop.
- There are no still lifes. A firing cell is required to stop firing, so nothing can persist unchanged.
Signals are natural; gates are not established
Directional packets are exactly the kind of signal a construction needs, and simple wires and delays can be built.
Excitable media
Nerve fibres and heart muscle share the key feature that produces this behaviour: after firing, a patch of tissue is briefly unable to fire again, so a wave of activity travels forwards and cannot reverse. Brian’s Brain reproduces that geometry with three states and no biology at all — it is an illustration of the mechanism, not a quantitative model of tissue.
Things to try
- Use the Firing and Refractory paint buttons in the dock to draw a channel, then start a packet at one end and watch it follow the channel.
- A closed ring drawn in firing cells will circulate. Try rings of different sizes and see which ones survive.
- Reduce Speed to 10 fps — the three-state cycle is hard to follow at full speed.