Analytic Theory of Fractal Growth Patterns in 2 Dimensions
| dc.creator | Davidovich, Benny | |
| dc.creator | Procaccia, Itamar | |
| dc.date | 2000-03-03 | |
| dc.date.accessioned | 2026-07-07T02:36:56Z | |
| dc.date.available | 2026-07-07T02:36:56Z | |
| dc.description | Diffusion Limited Aggregation (DLA) is a model of fractal growth that was introduced in 1981 and had since attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. Despite tremendous efforts there is no theory to compute the fractal dimension of DLA from first principles. In this Letter we offer such a theory for fractal growth patterns in two dimensions, including DLA as a particular case. In this theory the fractal dimension of the asymptotic cluster manifests iteself as a renormalization exponent observable already at very early growth stages. Using early stage dynamics we compute 1.6896<D<1.7135, and explain why traditional numerical estimates converged so slowly. We discuss similar computations for other fractal growth processes in 2-dimensions. | |
| dc.description | 5 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0003044 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0003044 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/16108 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Analytic Theory of Fractal Growth Patterns in 2 Dimensions | |
| dc.type | text |