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The description of the rescaled evolution set of p-Fermat cellular automata developed in the first part of this paper is applied for the calculation of the Hausdorff dimension of this set. The scaling procedure is analyzed and an appropriate scaling sequence for cellular automata with states in the integers modulo m is given. New proof of the main theorem… (More)
Coarse-graining invariant two-dimensional sequences, generated as orbits of oneand twodimensional cellular automata, were introduced in [Barbé et al., 1995] and further investigated in [Barbé, 1996, 1997]. Such sequences are invariant under a so-called coarse-graining operation which provides a particular way of rescaling a sequence. In its most simple… (More)
It has been observed that the long time evolution of a cellular automata (CA) can generate fractal sets. In this paper, we define a broad class of CA, all of which have a limit set. Moreover, we present an algorithm which associates with a CA of the above defined class a substitution system which deciphers the self-similarity structure of the limit set.