LACUNARITY OF RANDOM FRACTALS

We discuss properties of random fractals by means of a set of numbers that characterize their universal properties. This set is the generali zed singularity spectrum that consists of the usual spectrum of multif ractal dimensions and the associated complex analogs. Furthermore, non universal properties are recovered from the study of a series of funct ions which are generalizations of the so-called energy integral. (C) 1 997 Elsevier Science B.V.