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Fractal percolation and branching cellular automata
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  • Published: June 2001

Fractal percolation and branching cellular automata

  • F.M. Dekking1 &
  • P. v.d. Wal1 

Probability Theory and Related Fields volume 120, pages 277–308 (2001)Cite this article

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  • 2 Citations

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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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Authors and Affiliations

  1. Thomas Stieltjes Institute for Mathematics and Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands. e-mail: F.M.Dekking@its.tudelft.nl, P.vanderWal@its.tudelft.nl, , , , , , NL

    F.M. Dekking & P. v.d. Wal

Authors
  1. F.M. Dekking
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  2. P. v.d. Wal
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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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  • Issue Date: June 2001

  • DOI: https://doi.org/10.1007/PL00008784

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  • Mathematics Subject Classification (2000): Primary 28A80; Secondary 60J80
  • Keywords or phrases: Random fractal set – Fractal percolation – Multi-type branching process
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