Langton’s Ant Variants
The original Langton’s ant uses two colors and two rules: turn right on white, turn left on black. Extend the rule string to more characters and more colors emerge. “RLR” uses three colors, “LLRR” uses four. Some rules create highways, some fill space, some spiral into symmetric patterns. The rule string is the genome; the pattern is the phenotype.
The rule string
Each character in the rule string corresponds to a color state. “R” means turn right (clockwise), “L” means turn left (counterclockwise). When an ant lands on a cell of color i, it turns according to the ith character of the rule, changes the cell to color (i + 1) mod n, and advances one step. With two colors (RL), this is the original Langton’s ant.
Emergent behavior
Different rules produce dramatically different patterns. The classic RL produces chaos followed by an emergent highway. LRRL creates a highway almost immediately. RLLR spirals into a near-perfect square. LLRR fills space with a growing diamond. Longer rules produce increasingly intricate symmetries. Nobody has a general theory for predicting which rules produce which behavior.
Multiple ants
With multiple ants on the same grid, they interact through the shared state of the cells. Each ant follows its own rules independently, but their trails overlap and interfere, creating cooperative patterns that neither ant would produce alone.