Langton's Ant Turmite Explorer

About the specimen

Langton's Ant is a two-dimensional Turing machine devised by Christopher Langton in 1986. The machine is a single cell, the ant, walking a grid of square cells under one stubbornly simple instruction. Almost nothing about its rule hints at what it does.

Run it and the first few thousand steps look like noise, a lopsided symmetric smudge. Then near step ten thousand the disorder collapses into a repeating diagonal corridor, the highway, a cycle of 104 moves that the ant lays down forever. No one has found an initial pattern that stops it: the trajectory is provably unbounded (Cohen and Kong).

The ant is also a small universal computer. With the right starting cells it can be wired into logic gates, which means its long-term behaviour is, in general, undecidable. Order out of one rule, and no shortcut to predict it.

Turmites: one rule per colour

The explorer above generalises the ant into a turmite. Instead of two cell states it allows up to six, and you write one turn per state as a string of L, R and U. RL is the original ant; RLR never settles; LLRR grows a symmetric island; RRLL fills a tidy square. Change one letter and a different organism appears. Type your own and watch what it grows.

Reference: Langton's Ant and Turmite, Wikipedia. Built as a study, not a copy.