Cellular automata

[tsuki]

I wonder whether it fits to this sub-forum, but I find them endlessly fascinating.
Cellular automata are discrete models studied in computer science.

What they are is basically a lattice with cells that in the simplest form can either be dead or alive.
Then, there are rules that define whether a cell changes its state depending on the state on the nearest cells in its neighborhood.
For example, a cellular automaton called "Game of Life" is defined as such:

1. Any live cell with two or three neighbors survives.
2. Any dead cell with three live neighbors becomes a live cell.
3. All other live cells die in the next generation. Similarly, all other dead cells stay dead.

The lattice is then, either seeded with live cells randomly, or created manually to engineer specific behavior.

I find these automata to be fascinating because these rules are so easy to understand, and yet produce remarkable, life-like complexity.
Here are some examples:

Someone even understood these rules and built a programmable computer in it:

Mandelbrot set:

And finally, "Game of Life" described in terms of itself, simulated in itself:

 

There are other rule sets, also in 3 dimensions. This one is called "Accretor" and is simulated in a comprehensive program dealing with chaos theory: