Visualizing the Template of a Chaotic Attractor

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.