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. 1089–1126DOI 10.4171/RMI/590