Cellular

A row of cells, a rule about neighbours, and one line drawn per step. That’s all of it, and somewhere in the 256 ways of setting it up, it starts producing things nobody put there.

Rule 30 turns a single black cell into noise good enough that it once shipped as a random number generator. Rule 110 does something stranger: with a carefully constructed starting pattern, its cells can simulate a Turing machine. The rule is computationally universal. Most of the other 254 settle into stripes or die out. The interesting ones are easier to spot when you run them.

The measurements sit next to the pixels, so entropy and correlation stop being abstract numbers and become a caption for the picture you’re already looking at. Langton’s λ belongs to the rule table; the other numbers describe a particular run. Change the seed, width, or boundaries and those numbers can change. The chaotic/complex boundary is marked, including the places where classifications disagree.

Things to try

• Run rule 30 and then rule 31. Just one output bit changes; the pattern changes with it.
• Put rule 110 beside rule 90 and watch structure argue with symmetry.
• Sort by a metric and see which rules the numbers group together.
• Find the edge of the chaotic band and work along it.

Why it’s a speck

There’s nothing to win here. You’re browsing a zoo of very small machines, and you leave when you’re done.

Open Cellular