Abstract
On the basis of the premise that scaling is defined by a set of scaling transformations which form a simple product group, a scaling group is constructed for simple fractal scaling and the scaling of multifractal sets. The singularity strengths and densities are shown to be corollary to the scaling-group formalism. Fractal dimension and other exponents are shown to be generators of infinitesimal transformations. Applications are made to self-affine fractals and the scaling log-normal distribution.
- Received 10 March 1987
DOI:https://doi.org/10.1103/PhysRevLett.58.2786
©1987 American Physical Society