Shape of Fractal Growth Patterns: Exactly Solvable Models and Stability Considerations

Itamar Procaccia and Reuven Zeitak
Phys. Rev. Lett. 60, 2511 – Published 13 June 1988
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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 f(α) 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

Authors & Affiliations

Itamar Procaccia and Reuven Zeitak

  • Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel

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Vol. 60, Iss. 24 — 13 June 1988

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