Chaos And Fractal Software

Chaos and Fractal Software

Author(s): Jonathan Choate

Jonathan Choate

The College Mathematics Journal, Vol. 22, No. 1 (Jan., 1991), pp. 65-69.

Published by: Mathematical Association of America

Stable URL: http://www.jstor.org/stable/2686742

Tags: Software for differential equations and dynamical systems

Abstract: The article by Jonathan Choate is primarily a brief description of free or cheap software, from 1985 onward, for generating Mandelbrot sets and examining their properties and behavior. The article begins with a discussion of the relative crudeness of programs available at the time of its writing. Such programs primarily allowed for the generation of ‘dazzling’ pictures of Mandelbrot sets via relatively simple generation algorithms. While such algorithms prove favorable for machine performance and generation times, they are lacking in feature richness and dynamics for more granular analysis of the resulting systems. To combat the relative analytic sparseness of the available software, the article provides some examples of software with additional technical features and improved dynamic analysis tools. To provide efficient categorization of the software available for Mandelbrot set and chaotic dynamical systems analysis and to make it easier for the reader to find suitable software for their project, the author organizes the programs discussed into multiple brief feature-set overviews and a final table with qualitative descriptors for each of the features of interest to potential users. Mandelbrot sets and chaotic dynamical systems pose impressive mathematical challenges to the curious explorer, psychonaut or mathematician. The inherent complex symmetry and evolving behavior down to the finest levels of granularity has proven a fascinating problem space for new math knowledge and interesting analogies. However, the present software tools available for analyzing Mandelbrot sets, and indeed, researchers in the field of chaos and dynamical systems at large seem to gloss over the potential applications of chaos to self organizing real systems. Such understudied applications might include chaotic spike train events in en vivo neural ensembles, dynamic self organization of genetic sequences,protein expressions, and memetic complexes, explosive synthetic biological or purely artificial growth, in population volume and integrated information content among many others. Certainly, the possibilities for chaotic dynamical systems, Mandelbrot sets and their kin are vast and broad in scope, one might even venture to call the potential for chaos, to be, ironically, itself chaotic. Michael Thomas Lynn, Stephen F. Austin State University, May 2, 2017.

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