Numerical Experiments and Visualization of Chaos

Felipe Contreras-Alcala () and Alejandra Rosales-Lagarde ()
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Felipe Contreras-Alcala: Universidad Autonoma de la Ciudad de Mexico
Alejandra Rosales-Lagarde: CONAHCYT

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 193-214 from Springer

Abstract: Abstract The visualization of orbits and attractors of chaotic systems is a process that has been in progress for some time. Advances in computation, both in hardware and software, have made it increasingly easier, cheaper, and more visually appealing. However, all this pales in comparison to the speed with which new images are now produced using a recent personal laptop. This provides the dynamical systems researcher or data analyst with new possibilities to represent their data by trying multiple methods without wasting so much time, producing results that are both aesthetically pleasing and suitable for any professional presentation. The experiments shown here allow to explore some of these possibilities and open the way for new types of complex data representation, putting the emphasis on discerning hidden features in them. All images were programmed with Python and using the latest optimization and parallelization features available to display them quickly. Recent libraries such as datashader are also used for image display, which has proven its worth in accentuating the colors of the most used regions according to the required color map. Finally, the use of relatively simple mathematical transformations and higher dimensional representations is proposed, which can help to distinguish hidden features produced by an overuse of the same region of the image.

Keywords: Chaos; Attractor; Data; Visualization; Python; Enhancing (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16368-4_9

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