Simulations

Rules (B3/S23):

1. A dead cell with exactly 3 live neighbours is born.
2. A live cell with 2 or 3 survives.
3. Every other cell dies or stays empty.

Rules:

1. An off cell starts firing if exactly 2 of its 8 neighbours are firing.
2. A firing cell is dying in the next generation.
3. A dying cell switches off.

Brian Silverman's automaton: since no cell can keep firing, almost everything that survives is on the move. The simplest spaceship is two firing cells with two dying cells behind them, and it travels one cell per generation.

Rules:

1. Each termite wanders randomly: one square forward, then a small random turn.
2. Empty-handed, when it steps onto a wood chip, it picks it up and jumps away.
3. Carrying, it wanders until it steps onto another chip, then looks around for an empty square nearby and drops its chip there.
4. After dropping, it jumps away in random directions until it lands on an empty square, then starts searching again.

Order from chaos: no termite follows a plan, yet the chips gather into fewer and larger piles. Mitchel Resnick's model from StarLogo (1994).

The termite count takes effect at tick 0, or after Scatter chips / Clear.

Rules:

1. Each letter of the rule belongs to one square color, in order. The first one is the dark square.
2. The ant turns as the letter of its square says: R right, L left.
3. The square takes the next color (after the last one it turns dark again), then the ant steps forward.

A new rule takes effect at step 0, or after Clear.

Rules:

1. Grains of sand fall onto the board one by one.
2. A square holding 4 or more grains topples: it passes one grain to each of its four neighbours.
3. A toppling can make the neighbours topple too, setting off an avalanche that runs until every square holds 3 grains or fewer.
4. Grains pushed over the edge of the board are lost.

Bak, Tang and Wiesenfeld's model of self-organized criticality (1987): the pile tunes itself to a critical state where avalanches of every size occur. Dropped on a single spot, the grains build a fractal.

Rules:

1. The board is a single row of cells, and every generation is drawn below the previous one, so time flows downwards.
2. A cell's next state depends only on itself and its two neighbours, which gives 8 possible cases.
3. The rule table gives the new state for each case. Read as a binary number, its eight outputs give the number of the rule.

A new rule takes effect immediately. When the board fills up, it scrolls upwards.

Rules:

1. Every cell has one of the colors, which follow each other in a cycle: after the last one comes the first again.
2. A cell moves on to the next color if at least as many of its neighbours as the threshold already have that color.
3. Otherwise it keeps its color.

Changing the number of colors starts again from random noise. The threshold and the neighbours take effect immediately.

Rules:

1. An empty square stays empty.
2. An electron head becomes an electron tail.
3. An electron tail turns back into wire.
4. A wire square becomes an electron head if exactly 1 or 2 of its 8 neighbours are electron heads.

Brian Silverman's automaton (1987): electrons run along the wires, and with clocks, diodes and logic gates it can build a working computer.