Composition of Fractals
Metric Geometry
2020-10-20 v2 Geometric Topology
Abstract
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with segments of equal size, the composite dimension can be expressed as a function of the component dimensions. But in the case of the compositions including component multifractals, the composite dimension cannot be expressed as explicit function of component dimensions and can only be solved numerically. An application of fractal composition to a physics problem within the incomplete statistics is discussed.
Cite
@article{arxiv.1407.2859,
title = {Composition of Fractals},
author = {Yann Lanoiselee and Laurent Nivanen and Aziz El Kaabouchi and Qiuping A. Wang},
journal= {arXiv preprint arXiv:1407.2859},
year = {2020}
}
Comments
22 pages, 7 figures