Almost periodic CA

In Bert Hof and I have studied cellular automata acting on a class of quasiperiodic dynamical systems. A HTML version of the paper which appeared in NONLINEARITY Vol 8 (4) : 477-491 (1995). Usually, cellular automata are evolved on a finite phase space using periodic boundary conditions. We showed how to evolve quasiperiodic configurations. Periodic configurations can be treated like this also and allow to determine the evolution in encoded and compressed form. For experiments, we have a Mathematica source code available. As a SURF project 1995, Evan Reed (now at MIT) and I continued research on lattice gas automata. Here is the HTML version of our paper which appeared in Complex Systems 10 (1996), no. 3, 219-227.

The GifMovie shows almost periodic Life . The phase space is infinite, configurations are almost periodic. The computer evolves interval configurations and displays part of the infinite phase space, where one sees the familiar Life evolution. The displayed configuration appears again and again in the two dimensional plane but not in a periodic way. During the evolution the complexity of the configurations grow in the sense that we need more and more intervals to store the configuration. The growth rate measures an entropy for the almost periodic system .

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