MULTIFRACTALS DEFINED BY NONLINEAR CELLULAR-AUTOMATA

It is known that the space-time output patterns of additive cellular a utomata may be scaled to yield fractals. In this paper, nonadditive ce llular automata rules are grouped into equivalence classes, each class defined in terms of a characteristic nonadditive rule. This rule defi nes a multifractal uniquely associated to each class. It is shown that these multifractals can be generated by a form of matrix substitution system, called concatenation substitution. This allows easy computati on of fractal dimensions. It is likely that the multifractal spectra f or each class does not possess the usual inverted U shape. A conserved quantity is found to be associated with the concatenation substitutio n system, and is shown to play a role similar to Langton's lambda-para meter.