Lyapunov exponents of the Mandelbrot set (The mini-Mandelbrot)

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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.

    hawkexpress, jim.windle, voxel123, and 5 other people added this photo to their favorites.

    1. Talfrac [deleted] 72 months ago | reply

      Hi, I'm an admin for a group called FractArt - Fractals as Art, and we'd love to have this added to the group!

    2. Fractal Ken 72 months ago | reply

      Interesting image and explanation. The background provides a good feeling of depth.

      Seen in:
      FractArt - Fractals as Art

    3. Evi_1 52 months ago | reply

      mandelbrot set, fractals... damn, i love it!..

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