Mandelbrot

Okay, it’s time to feed the eyes with many amazing things…

Mandelbrot, fractal geometry and chaos theory are intricately related and it all got me very excited back in 1996 when one could acquire a little disk with a programme that generated Mandelbrot designs ad infinitum. Then I went and had my mind bewitched at a lecture at the University of Natal (then) in Durban, by attending a lecture on Clocks and Clouds ((Euclidean vs. fractal geometry)…. how the world of fractal geometry is all about similar but not the same, like the leaves on a tree, which are identifiable but not identical.

Mandelbrot discovered an underlying order in apparent randomness. Fractal geometry is the underlying law that causes the similarities in appearance between cream flowing into coffee and a glacier slowly making its way across a landscape on a satellite image; the course of the pattern in a kudu horn and water going down a plughole; the random patterns of stars in the skies and daisies in a field…there are laws as immutable as Euclidean geometry but with more ‘play’.

Aaaaaaaaaaaaaanyway:  the amazing Benoit Mandelbrot who added so much to my life and those of many others has died recently. But what a legacy to leave! Read more about him here: http://www.escapestudios.co.uk/celebrating-mandelbrot-beautiful-3d-images/ for the latest developments in fractal applications. One of the beautiful pics appears on the left, as an appetiser.

More on the historical background of Mandelbrot and his work can be found here –  and here’s an excerpt:

‘The erratic behavior that had showed up in incomes and cotton prices had also appeared in physics in Brownian motion and other forms of behavior of fluids and gases and in Mandelbrot’s earlier work with the telephone circuits.  “In geometry, it showed up in patterns that were made of tiny clumps that were distributed seemingly randomly. The patterns lacked the neatness of the straight lines and smooth curves of Euclidean geometry, but the patterns were self-similar, that is, if one magnified the pattern, each part looked like a miniature copy of the whole.”  This could be done indefinitely, moving to a smaller and smaller scale. Mandelbrot used the word fractal (meaning fractured or broken up) to describe these geometric patterns.’

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