Abstract
Fractal, dendritic patterns with invariant distributions which are harmonic measures are represented by Julia sets of polynomial mappings. The equipotential lines around such patterns are obtained, leading to analytic estimates of the minimal and maximal scaling exponents of the function of the harmonic measure. These and physical stability arguments rationalize the shapes of diffusion-limited aggregates.
- Received 1 February 1988
DOI:https://doi.org/10.1103/PhysRevLett.60.2511
©1988 American Physical Society