A DIMENSION FORMULA FOR SELF-SIMILAR AND SELF-AFFINE FRACTALS

A geometric and very general relation between the size distribution an d the fractal dimensions of a set of objects is presented. The applica tions are numerous, ranging from fragmentation experiments to time ser ies. For example, it may be used to understand the fragment-size distr ibution of fragmenting gypsum. The formalism also generalizes to self- affine fractals, and here it is applied to the scaling properties of s elf-interactions in (1+1)-d directed percolation.