Embedding computation in one-dimensional automata by phase coding solitons

It is shown that some kind of meaningful computation can be embedded in very simple, microscopically homogeneous, one-dimensional automata, and in particular filter automata with a parity next-state rule. A systematic procedure is given for generating moving, periodic structures (particles). These particles exhibit soliton-like properties; that is, they often pass through one another with phase shifts. Ways to encode information in the phase of these particles are discussed. The search for useful logical operations is reduced to a search for paths in certain graphs. As a demonstration of principle, the details of implementing a carry-ripple adder are given.>