  In this work we are interested in the self--affine fractals studied by
Gatzouras and Lalley and by the author which generalize the famous general
Sierpinski carpets studied by Bedford and McMullen. We give a formula for the
Hausdorff dimension of sets which are randomly generated using a finite number
of self-affine transformations each one generating a fractal set as mentioned
before, with some technical hypotheses. The choice of the transformation is
random according to a Bernoulli measure. The formula is given in terms of the
variational principle for the dimension.
