Computing fractal dimensions for additive cellular automata
Efficient methods are given for finding the statistics of symbol blocks occurring in the graphs of additive cellular automata after large numbers of iterations. In particular, the methods yield fractal dimensions, entropies, and a recurrence relation for the number of nonzero symbols. The methods are based on the construction of a nonnegative integer matrix A closely related to the automaton. The largest eigenvalue of A tells the fractal dimension, while the corresponding eigenvector gives the relative frequencies of blocks.
scientific article; zbMATH DE number 4033086
scientific article