Try to **explore** a bit: zoom out, scroll around. Get a sense for the chaotic, fleeting structures—those seams of little "spaceships"—and for their more humdrum compatriots that linger unchanged on the outer diagonal.

They are all part of a machine, a one-dimensional cellular automaton with the power, unbelievably, of a universal computer. It is thought to be the simplest there is.

Eight rules determine every pattern on this page and its infinite extension:

That such a compact description of a world could seed the kind of genuine mathematical complexity required to (among other things) decide every recursively enumerable language is downright astonishing, and, I think, well worth a look.

1. The rules tell cell*x* what color he should be based on the three cells in the row above him (at 11, 12, and 1 o'clock). See the Wikipedia pages for **rule 110** and **universal computer** to learn more.

2. Hit**spacebar** to generate more rows.

They are all part of a machine, a one-dimensional cellular automaton with the power, unbelievably, of a universal computer. It is thought to be the simplest there is.

Eight rules determine every pattern on this page and its infinite extension:

{◼◼◼ => ◻ | ◼◼◻ => ◼ | ◼◻◼ => ◼ | ◼◻◻ => ◻ | ◻◼◼ => ◼ | ◻◼◻ => ◼ | ◻◻◼ => ◼ | ◻◻◻ => ◻}^{1}

That such a compact description of a world could seed the kind of genuine mathematical complexity required to (among other things) decide every recursively enumerable language is downright astonishing, and, I think, well worth a look.

1. The rules tell cell

2. Hit