Self-Similar Functions Generated by Cellular Automata
Heinz‐Otto Peitgen, Anna Rodenhausen, Г. Скордев · Fractals · 1998
The self-similarity properties of the functions (closed relations) associated with one- and two-sided cellular automata are studied. It turns out that these functions are generated by sequential machines, and their graphs are fractal sets generated by hierarchical iterated function systems. The Hausdorff dimensions of the graphs is one for one-sided cellular automata and two for two-sided automata.