Hamming sets, Ising sets, cellular automata, neural nets, and the random walk Available to Purchase

Cellular automata and neural nets are nonlinear dynamical systems of interest to physicists as models of computational devices and physical processes. The possible states of both N‐cell automata and N‐binary‐neuron networks can be represented by the 2^N corners of the unit hypercube (the Hamming set) in N‐dimensional space. This representation is transparently related to the representation of the states of N spin‐one‐half particle systems and of N‐step random walks by strings of positive and negative ones (the Ising set). The dynamics of discrete neural networks and cellular automata can be described by the 2^N by 2^N transition matrices which describe the mappings of the Hamming set and Ising set into themselves. This representation renders some properties of these nonlinear systems readily apparent, and highlights their relation to the lattice gas, systems of interacting spins, and the random walk.