File:Lyapunov exponents of the Mandelbrot set (The mini-Mandelbrot) - Matlab.png

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The Lyapounov exponent measures how rapidly orbits diverge from each other. Here I calculated it approximatively for the Mandelbrot set.

Points inside the set converge to various cycles and hence have negative exponents. The shining centers of the components are the points that are right on a cycle. Points outside diverge to infinity, and have positive exponents. The unseen but intricate border includes both chaotic and periodic points.
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Source Lyapunov exponents of the Mandelbrot set (The mini-Mandelbrot)
Author Anders Sandberg from Oxford, UK

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This image was originally posted to Flickr by Arenamontanus at https://www.flickr.com/photos/87547772@N00/3408610381. It was reviewed on 25 November 2011 by FlickreviewR and was confirmed to be licensed under the terms of the cc-by-2.0.

25 November 2011

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current13:32, 25 November 2011Thumbnail for version as of 13:32, 25 November 2011801 × 801 (485 KB)Jacopo Werther (talk | contribs){{Information |Description= The Lyapounov exponent measures how rapidly orbits diverge from each other. Here I calculated it approximatively for the Mandelbrot set. Points inside the set converge to various cycles and hence have negative exponents. The s

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