Golden mean arithmetic in the fractal branching of diffusion-limited aggregates
- 8 June 1992
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 68 (23) , 3456-3459
- https://doi.org/10.1103/physrevlett.68.3456
Abstract
We use the wavelet transform microscope to explore the intricate fractal geometry of Witten and Sander’s diffusion-limited aggregates. We report on the discovery of Fibonacci sequences in the internal hierarchical structure of these clusters. We discuss the relevance of the golden mean arithmetic to the numerically well established statistical self-similarity of these aggregates.Keywords
This publication has 22 references indexed in Scilit:
- Branch order and ramification analysis of large diffusion-limited-aggregation clustersPhysical Review A, 1992
- Comment on ‘‘Self-similarity of diffusion-limited aggregates and electrodeposition clusters’’Physical Review Letters, 1989
- Argoulet al.replyPhysical Review Letters, 1989
- Self-Similarity of Diffusion-Limited Aggregates and Electrodeposition ClustersPhysical Review Letters, 1988
- Structure of large two-dimensional square-lattice diffusion-limited aggregates: Approach to asymptotic behaviorPhysical Review A, 1987
- Universality, nonuniversality, and the effects of anisotropy on diffusion-limited aggregationPhysical Review A, 1986
- Anisotropy and Cluster Growth by Diffusion-Limited AggregationPhysical Review Letters, 1985
- Internal structure of diffusion-limited aggregatesPhysical Review A, 1985
- Diffusion-limited aggregationPhysical Review B, 1983
- Diffusion-Limited Aggregation, a Kinetic Critical PhenomenonPhysical Review Letters, 1981