Math
Langton's ant
Run Langton’s ant on a sparse unbounded lattice, change multicolour turn rules and inspect the classic 104-step highway.
Try this
On each cell: turn according to its colour, advance its colour cyclically, then move one square. RL on a blank grid develops a repeating highway after a long transient. Other rule strings can behave differently. The sparse grid has no wraparound; each run stops at one million steps.
Equations used in the module
Equations Rule[state] determines left or right turn state ← (state+1) mod number of rule symbols The ant moves one unit in its new direction Classic RL highway: 104-step cycle with a translated local pattern
