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Cellular Automata With Almost Periodic Initial Conditions

Bert Hof
Organization: McMaster University
Oliver Knill
Organization: Harvard University
Department: Department of Mathematics
URL: http://abel.math.harvard.edu/~knill/
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Part of the following mathematica procedures have been used to make experiments and illustrations to our preprint `A.Hof and O.Knill, Cellular automata with almost periodic initial conditions' which is to appear in the journal "Nonlinearity". The programs allow to investigate CA on circle subshifts as described in the article. The present notebook has implemented procedures which allow to treat the following situations:

* One dimensional elementary CA. * One dimensional CA with radius of interaction r=2. * Two dimensional CA,(Life). * The HPP lattice gas CA. * The HPP lattice gas CA with obstacles. * The HPP lattice gas CA with mirrors. * The three dimensional HPP lattice gas CA (nondeterministic collisions). * The hexagonal lattice gas CA (nondeterministic collisions). * The hexagonal lattice gas CA with obstacles (nondeterministc) collisions).

The programs can easily be modified to treat other situations. One could consider for example three dimensional situations with obstacles or CA in higher dimensions or CA lattice gas automata with different kind of particles or different kind of mirrors.

*Mathematics > Discrete Mathematics > Cellular Automata

Cellular automata, Almost periodicity, Topological dynamics, Subshift, Game of Life, Lattice gas cellular automata, Hexagonal lattice gas cellular automata, HPP lattice gas cellular automata
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cellular.m (19.2 KB) - Mathematica package