Tensor-generated fractals: Using tensor decompositions for creating self-similar patterns
General Mathematics
2018-12-04 v1
Abstract
The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this paper, we will present a method for the construction of geometric fractals that exploits Kronecker products and tensor decompositions, which can be regarded as a generalization of matrix factorizations. We will show how to create several well-known examples for one-, two-, and three-dimensional self-similar structures. Additionally, the proposed method will be extended to the construction of fractals in arbitrary dimensions.
Cite
@article{arxiv.1812.00814,
title = {Tensor-generated fractals: Using tensor decompositions for creating self-similar patterns},
author = {Patrick Gelß and Christof Schütte},
journal= {arXiv preprint arXiv:1812.00814},
year = {2018}
}