Langtons ant is a popular cellular automaton. It is interesting to me because I am often fascinated by the way that complex patterns can form from a set of very simple rules. You can read about it on Wikipedia. or watch the Numberphile video. After watching the Numberphile video I got interested in the possible patterns that might emerge when Langtons Ant is not walking atop a plane made of squares, but out of hexagons.

The rules for this version are identical to the original version. When the ant lands on a new tile, it does the following:

  • Turn left or right, depending on whether the tile is black or white
  • Flip the color of the tile
  • Move one tile forward

I did not do any deep analysis on this, other than staring on the animation, but the pattern that emerges seems to be very symmetrical along a diagonal axis.