An algorithm that yields textured and connected binary fractals is presented. The texture is imposed by modeling the fractal as a Markov random field (MRF) at every resolution level. The model size and the parameters specify the texture. The generation starts at a coarser level and continues at finer levels. Connectivity, which is a global property, is maintained by restricting the flow of the sample generating Markov chain within a limited subset of all possible outcomes of the Markov random field. The texture is controlled by the parameters of the MRF model being used. Sample patterns are shown.