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Lyapunov exponents of the Mandelbrot set (Steel Beach)

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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Uploaded on April 3, 2009