Visualizing the Template of a Chaotic Attractor

TL;DR

This paper introduces a new tool for validating, optimizing, and visualizing templates of chaotic attractors bounded by a genus-1 torus, enhancing understanding of their topological structure.

Contribution

It presents a novel method for validating linking matrices, optimizing template compactness, and generating SVG visualizations of chaotic attractor templates.

Findings

Validated linking matrices for chaotic attractors

Optimized template compactness and minimal height

Generated scalable vector graphics visualizations

Abstract

Chaotic attractors are solutions of deterministic processes, of which the topology can be described by templates. We consider templates of chaotic attractors bounded by a genus-1 torus described by a linking matrix. This article introduces a novel and unique tool to validate a linking matrix, to optimize the compactness of the corresponding template and to draw this template. The article provides a detailed description of the different validation steps and the extraction of an order of crossings from the linking matrix leading to a template of minimal height. Finally, the drawing process of the template corresponding to the matrix is saved in a Scalable Vector Graphics (SVG) file.