The Mystery of Langton's Ant and the Cardioid

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Directions:
How the Ant moves:
New Features:
What is known:


(*The conjecture:
*)

Here is a good reference on Langton's Ant:
D. Gale, J. Propp, S. Sutherland, S. Troubetzkoy
Further travels with my ant.
Mathematical Intelligencer 17 (1995), no. 3, 48--56.

Among other things, they demonstrate this reflective symmetry property of some Ants. A while back I wrote a similar proof of this fact. It is available here.

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