  How many fractals exist in nature or the virtual world In this work, we
partially answer the second question using Mandelbrots fundamental definition
of fractals and their quantities of the Hausdorff dimension and Lebesgue
measure. We prove the existence of beth-two of virtual fractals with a
Hausdorff dimension of a bivariate function of them and the given Lebesgue
measure. The question remains unanswered for other fractal dimensions.
