HAUSDORFF DIMENSION OF CERTAIN RANDOM SELF-AFFINE FRACTALS

摘要

In this work we are interested in the self-affine fractals studied by Gatzouras and Lalleyn[5] and by the author [11] who generalize the famous general Sierpinski carpets studiednby Bedford [1] and McMullen [13]. We give a formula for the Hausdorff dimension ofnsets which are randomly generated using a finite number of self-affine transformationsneach generating a fractal set as mentioned before. The choice of the transformation isnrandom according to a Bernoulli measure. The formula is given in terms of the variationalnprinciple for the dimension.