Multi-fractal multi-resolution structures from DLA - Strange Attractors Hybrids

摘要

In this paper we propose and simulate novel multi-fractal multi-resolution structures, which arise when hybrid schemes formed by Diffusion Limited Aggregation (DLA) and Strange Attractors (SA) are considered. First, DLA aggregates formed with a given attachment radio (R-a) are generated so that a particle is attached to the aggregate as soon as it is at a distance R-a from any other particle in it. Second, a randomly chosen SA substitutes each particle of the aggregate, by means of a translation and a homothety with uniform scaling 1/R-a, which preserves the SA shape and circumscribes it to the circle of radius R-a. In this process, each SA is adjusted (re-normalized) to the R-a size. The resulting object mimics a cluster of SA, and exhibits a multi-fractal, multi-resolution structure, with a low-resolution profile similar to that of the DLA aggregate, but composed by SA fractals when a higher resolution is considered. We also describe an iteration of this process in order to generate hybrid superclusters, formed by clusters of DLA-SA hybrids. (C) 2019 Elsevier B.V. All rights reserved.