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what is the Mandelbrot set?
By Nik Dayman of teamfresh
Well this is a question that does not come with a short answer! take a look at the image of the complete set... When you look at the complete set, there is a curious black shape in the middle. It is actually one of an infinite amount of gaps that are contained within the Mandelbrot set. The Mandelbrot fractal set itself, is named after Benoît Mandelbrot. It is basically a graph. It is a set of points plotted in the complex plane. These points are placed upon the plane and a mathematical formula involving complex numbers is used to decide the placements of these points. The points create an image on the graph, The boundary of which forms a fractal. When computed and graphed on the complex plane, the Mandelbrot Set is seen to have an extremely elaborate boundary, which does not simplify at any given magnification! This means however much you enlarge the graph, and magnify the elaborate boundary, it contains ever more complex details inside itself. So now you know that the Mandelbrot set is infinitely complex, and the boundary qualifies as a fractal. If you go exploring deep inside The Mandelbrot set, you will find that it is self-similar at magnified scales, but the small scale details are never identical to the whole. Each one is more complex than the last. The deeper you go inside the boundary, the more complex it gets. And it never ends. |
The complete Mandelbrot fractal set.
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