This paper studies the Hausdorff dimensions of random non-self-similar fractals. Here, we obtain the Hausdorff dimensional estimates of random net fractals generated by random contractions (including random transformation contraction and random ratio contraction). In addition, we give the...

Fractals and measures are often defined in a constructive way. In this paper, we give the construction of random measures concentrated on random Markov-self-similar fractals and prove that under quite weak conditions random Markov-self-similar measures exist and satisfy certain self-similarity...