POTENTIAL-THEORY AND ANALYTIC PROPERTIES OF SELF-SIMILAR FRACTAL AND MULTIFRACTAL DISTRIBUTIONS

By the use of recursion relations and analytic techniques we deduce ge neral analytic results pertaining to the electrostatic potential, mome nts, and Fourier transform of exactly self-similar fractal and multifr actal charge distributions. Three specific examples are given: the bin omial distribution on the middle-third Cantor set, which is a multifra ctal distribution, the uniform distribution on the Menger sponge, whic h illustrates the added complication of higher dimensionality, and the uniform distribution on the von Koch snowflake, which illustrates the effect of rotations in the defining transformations.