Abstract.
Branching cellular automata (BCA) are introduced as generalisations of fractal percolation by admitting neighbour dependence. We associate sequences of random sets with BCA's and study their convergence. In case of convergence we derive the Hausdorff dimension of the limit set and of its boundary. To accomplish the latter we proof that the boundary of a set generated by a BCA is again a set generated by a BCA.
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Received: 7 October 1999 / Revised version: 25 August 2000 / Published online: 26 April 2001
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Dekking, F., v.d. Wal, P. Fractal percolation and branching cellular automata. Probab Theory Relat Fields 120, 277–308 (2001). https://doi.org/10.1007/PL00008784
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DOI: https://doi.org/10.1007/PL00008784