Combinatorial Dynamics

David Hillman

The idea of combinatorial dynamics is to define sets of n-dimensional combinatorial spaces in as general way as possible, and then to find elementary local invertible maps T:A->B between pairs of space sets so that all local invertible maps are generated by the elementary ones. Then if T:A->A is a local invertible map, its orbits {T^z x : z in Z} (for each space x in A) are (n+1)-dimensional combinatorial spacetimes. These systems include reversible cellular automata but are much more general: geometry can change over time; big bangs are possible. I’ll  introduce these ideas by looking in detail at the one-dimensional case.

Created by Mathematica  (April 20, 2004)