OFFSET
0,3
COMMENTS
Rules for Langton's ant on edge-to-edge tilings by regular polygons: Initially, all tiles are white. On a white tile turn right, on a black tile turn left. Always flip the color of the tile, then move forward one unit. The turn angle for (triangle, square, hexagon, octagon, dodecagon) is (60, 90, 60, 45, 30).
At n=66285 the ant starts a highway along the SE diagonal.
Many other starting positions are possible which give different terms. While they all eventually enter the highway a(n+39) = a(n)+13, the generation where it happens varies (3328, 25256, 66285, 177723, 255119, 354465, 415327).
LINKS
Lars Blomberg, Table of n, a(n) for n = 0..10000
Lars Blomberg, Illustration of the tiling
Lars Blomberg, State when the highway goes outside the limit
FORMULA
a(n+39) = a(n)+13 for n > 66285.
CROSSREFS
KEYWORD
nonn
AUTHOR
Lars Blomberg, Aug 29 2019
STATUS
approved