Random fractals and tree-indexed Markov chains

  • Arnaud Durand

    Université Paris-Sud, Orsay, France


We study the size properties of a general model of fractal sets that are based on a tree-indexed family of random compacts and a tree-indexed Markov chain. These fractals may be regarded as a generalization of those resulting from the Moran-like deterministic or random recursive constructions considered by various authors. Among other applications, we consider various extensions of Mandelbrot’s fractal percolation process.

Cite this article

Arnaud Durand, Random fractals and tree-indexed Markov chains. Rev. Mat. Iberoam. 25 (2009), no. 3, pp. 1089–1126

DOI 10.4171/RMI/590