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How Benoit Mandelbrot Discovered #Fractals: A Short Film by Errol Morris I #complexity

How Benoit Mandelbrot Discovered #Fractals: A Short Film by Errol Morris I #complexity | e-Xploration | Scoop.it
Documentary filmmaker Errol Morris talked with Benoit Mandelbrot about the origins of fractals in 2010, only 19 days before the mathematician's death. You can watch the short film online.
luiy's insight:

Even if you know little of mathematics, you probably have some awareness of fractals. You’ve almost certainly heard them invoked, correctly or otherwise, to describe things that look or act the same at the large scale as they do at the small. You may even know the name Benoit Mandelbrot, the much-laureled Polish-French-American “father of fractal geometry.” Hard science-fiction titan Arthur C. Clarke called his eponymous set of mathematical points “one of the most astonishing discoveries in the entire history of mathematics.” Nassim Nicholas Taleb, the famously discriminating author of The Black Swan, called him ”the only person for whom I have had intellectual respect.” Even former French president Nicolas Sarkozy gave Mandelbrot his props, crediting his discoveries of the geometrical regularities of “rough” things, from coastlines to stock-market fluctuations, as antecedent to modern information theory. He also acknowledged Mandelbrot’s having carried on his work “entirely outside mainstream research,” and the mathematician’s reputation as an unusually insightful intellectual maverick survives him.

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The #sierpinski triangle page to end most sierpinski triangle pages | #patterns #fractals #dataviz

The #sierpinski triangle page to end most sierpinski triangle pages | #patterns #fractals #dataviz | e-Xploration | Scoop.it

Via Claudia Mihai
luiy's insight:
Constructing the Sierpinski triangle

Throughout my years playing around with fractals, the Sierpinski triangle has been a consistent staple. The triangle is named after Wacław Sierpiński and as fractals are wont the pattern appears in many places, so there are many different ways of constructing the triangle on a computer.

All of the methods are fundamentally iterative. The most obvious method is probably the triangle-in-triangle approach. We start with one triangle, and at every step we replace each triangle with 3 subtriangles:

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