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

## TL;DR

This paper introduces a novel method for generating geometric fractals using tensor decompositions and Kronecker products, enabling the creation of self-similar patterns across multiple dimensions.

## Contribution

It presents a new tensor-based approach for fractal construction, generalizing matrix factorizations to higher dimensions and broadening the scope of fractal generation techniques.

## Key findings

- Successfully generated classic fractals in 1D, 2D, and 3D
- Extended the method to arbitrary dimensions
- Demonstrated the versatility of tensor decompositions in fractal creation

## 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.