Combinatorial Dynamics
David Hillman
The idea of combinatorial dynamics is to define sets of ndimensional 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 onedimensional case.
Created by
Mathematica
(April 20, 2004)
