An odometer (aka an adding machine) is the "+1" map on a countable product of finite cyclic groups, indexed by {1,2,...}, addition with "carrying." Think of an old-fashioned car odometer with spinning wheels. Odometers are isometries.

A two-sided, one-dimensional cellular automaton is a map given by a "local rule" on all doubly infinite sequences with entries from a finite alphabet. In two dimensions, think of the Game of Life. In general, cellular automata are far from being isometries, and can be many-to-one.

I will explain what all the words mean and why many odometers can be embedded in cellular automata.

This is joint work with Reem Yassawi, Trent University (Canada).

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