How does an 86-cell loop with 8 possible cell states copy itself? The arm grows from the loop's corner, turns left three times and closes. The daughter is cut free at tick 151.
Try this Pause at about tick 140 and step one tick at a time to watch the arm close and the link to the mother loop get cut at tick 151.
About this model Where it ends up The run doesn't end, but it stops changing much. Once the torus is packed with loops, live-cells holds near 2,080 and no new loops appear.
John von Neumann's self-reproducing automaton needed 29 states and a universal constructor. Christopher Langton (Physica D, 1984) gave up universality and found a loop that copies itself using 8 states and a 5-cell neighbourhood. It became a standard example in artificial life, a field Langton named a few years later.
The loop is a core (state 1) inside a sheath (state 2). Signals travel around the core in pairs: 7-0 signals extend the arm and 4-0 signals turn it left. At the junction each signal is copied into the arm as well as continuing round the loop. After the arm has turned three times it closes into a daughter loop, the link is cut, and both loops start over. This version applies Langton's transition table synchronously on a 71 × 71 torus, with each rule applied in all four rotations.
Idea Christopher G. Langton
MathPets MathPets · org