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.
"Random fractals and tree-indexed Markov chains." Rev. Mat. Iberoamericana 25 (3) 1089 - 1126, October, 2009.