Tracks emerging by forcing Langton's ant with binary sequences

Abstract

The well-known "ant" defined by C Langton on a grid with black and white squares is forced by periodical binary sequences {r(m)}, as follows: i) The ant turns 90 degrees to the left (right) if it enters a white (black) square and if {r(m)} = 0 (Langton's case); and ii) the directions are reversed if {r(m)} = 1; in both cases the color of the square is inverted as the ant proceeds. Changing the sequences {r(m)} we obtain a plethora of different, periodical tracks. Thousands of runs, some of them differing only by one bit, never rendered the same pattern. Also, an ant moving from a white to a black domain may experience reflection, refraction or sliding on the black-white-border.