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Benoit Mandelbrot: Fractals and the art of roughness

Benoit Mandelbrot: Fractals and the art of roughness

http://www.ted.com/talks/benoit_mandelbrot_fractals_the_art_of_roughness.html

Related:  cienciaFractal GeometryFractals Mandlebrots & Dreams of Electric Sheep

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100 - Fractal Geometry Geometry. Its principles are taught to young students across the world. The Pythagorean theorem. Surface area and volume. Pi. Hunting the Hidden Dimension NOVA explores the fascinating world of fractals and looks at how they can be used to better understand everything from coastlines and rainforests to weather systems and human physiology.

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Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal Opening Pandora's Box For the Second Time ur story starts with a guy named Rudy Rucker, an American mathematician, computer scientist and science fiction author (and in fact one of the founders of the cyberpunk science-fiction movement). Around 20 years ago, along with other approaches, he first imagined the concept behind the potential 3D Mandelbulb (barring a small mistake in the formula, which nevertheless still can produce very interesting results - see later), and also wrote a short story about the 3D Mandelbrot in 1987 entitled "As Above, So Below" (also see his blog entry and notebook). Back then of course, the hardware was barely up to the task of rendering the 2D Mandelbrot, let alone the 3D version - which would require billions of calculations to see the results, making research in the area a painstaking process to say the least.

A Radical Mind Posted 10.01.08 NOVA "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." So writes acclaimed mathematician Benoit Mandelbrot in his path-breaking book The Fractal Geometry of Nature. Instead, such natural forms, and many man-made creations as well, are "rough," he says. To study and learn from such roughness, for which he invented the term fractal, Mandelbrot devised a new kind of visual mathematics based on such irregular shapes.

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Fractals (VLab: Virtual Complexity Lab) Author: Greg Paperin. Fractals are, roughly speaking, objects that exhibit self-similarity on all scales. Self-similarity means that an object consists of smaller copies if itself, which in turn, consist of smaller copies, and so on. The copies do not need to be exact, but the same kind of structures must appear on all scales. Commonly, fractals are mathematical objects, but many natural objects that demonstrate self-similarity on power-law scales are also considered fractals. This includes surfaces of clouds, mountains and other landscape entities, surfaces of plant structures and various other phenomena.

That's why he was a genius---he knew and didn't tell. by judearnold Apr 21

A genius, but he fails at explaining how it works for us mortals by mamc2501 Sep 12

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