The equality of fractional dimensions for certain cellular automata
A study is made of the development of certain cellular automata with apparently chaotic behavior. Results are obtained for cellular automata arising from additive rules modulo 2. For the corresponding limit sets it is shown that the growth rate dimension, the Kolmogorov dimensions, and the Hausdorff dimensions all coincide. This dimension is moreover independent of the choice of finite initial seed and the sampling times used. These cellular automata thus provide tractable test cases for the production of fractals by local processes.
scientific article; zbMATH DE number 4033085
scientific article