Monday, November 15, 2010

Clouds are not Spheres

Yes, as you read "... 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..". This was how Benoit Mandelbrot tried to explain how traditional geometry can not completely describe the geometry of things in nature.
To overcome this limitation he developed a new mathematical object called "Fractal".  Fractal is a mathematical object which among other properties has the property of self-similarity, i.e the object presents the same shape, pattern, form at different scales. Its importance has been proven in many areas of human life : Medicine, Economy, Technology (image, audio compression), etc.
Mandelbrot set inward zoom
Well, such object was not completely new to mathematicians but it was Mandelbrot who really took advantage of the technology of the 70's (the power of computers) and opened a new world in mathematics with Fractals.
Sierpinsky Triangle
Here goes my modest post salute to him after one month of his death (I was not catching up with my emails until today I realized of his death).

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