Structural five-fold symmetry in the fractal morphology of diffusion-limited aggregates
| Autor: | M. Tabard, Alain Arneodo, Françoise Argoul, J. F. Muzy |
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| Rok vydání: | 1992 |
| Předmět: |
Statistics and Probability
Fibonacci number Branching fraction Wavelet transform Geometry Multifractal system Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas Fractal 0103 physical sciences Probability distribution Golden ratio Statistical physics Snowflake 010306 general physics Mathematics |
| Zdroj: | Physica A: Statistical Mechanics and its Applications. 188:217-242 |
| ISSN: | 0378-4371 |
| DOI: | 10.1016/0378-4371(92)90269-v |
| Popis: | The statistical self-similarity of the geometry of diffusion-limited aggregates and the multifractal nature of the growth probability distribution on the surface of the growing clusters are investigated using the wavelet transform. This study reveals the existence of a predominant structural five-fold symmetry in the internal frozen region as well as in the active outer region of the interface. This observation is corroborated by a statistical analysis of the screening effects that govern diffusion-limited aggregation (DLA) growth in linear and sector-shaped cells. The existence of this symmetry is likely to be a clue to a hierarchichal fractal ordering. We report on the discovery of Fibonacci sequences in the inner extinct region of large mass off-lattice DLA clusters, with a branching ratio which converges asymptotically to the golden mean. We suggest an interpretation of the DLA morphology as a “quasifractal” counterpart of the well-ordered snowflake fractal architecture. |
| Databáze: | OpenAIRE |
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