Tensor-generated fractals: Using tensor decompositions for creating self-similar patterns

2018/11/30 by Gelß, Patrick, Schütte, Christof
#15A69 #28A80 #37F35 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.1812.00814

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.

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