## Institute for Mathematical Sciences

## Preprint ims95-1

** D. Gale, J. Propp, S. Sutherland, and S. Troubetzkoy**
* Further Travels with my Ant*

Abstract: We discuss some properties of a class of cellular automata sometimes called a "generalized ant". This system is perhaps
most easily understood by thinking of an ant which moves about
a lattice in the plane. At each vertex (or "cell"), the ant
turns right or left, depending on the the state of the cell,
and then changes the state of the cell according to certain
prescribed rule strings. (This system has been the subject of
several Mathematical Entertainments columns in the Mathematical
Intelligencer; this article will be a future such column). At
various times, the distributions of the states of the cells for
certain ants is bilaterally symmetric; we categorize a class of
ants for which this is the case and give a proof using Truchet
tiles.

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