Hausdorff dimensions of random net fractals11Project is partially supported by the Tian Yuan Foundation of China and Ph.D. Station Foundation of State Education Committee.

AbstractThis 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 definition of a random cookie-cutter set in R1 and obtain its dimension formula