Fractals

Fractals Fractional Dimension Dr. Benoit Mandlebrot proposed the idea of a fractal, which is short for "fractional dimension" as a way to cope with problems of scale in the real world. He defined a fractal to be any curve or surface that is independent of scale. This property, which is called self-similarity, means that any portion of the curve, if blown up in scale, would appear identical to the whole curve. Meaning, the transition from one scale to another can be represented as iterations of a scaling process. The idea of self-similarity means that if we shrink or enlarge a fractal pattern, its appearance should remain unchanged. On the other hand, fractal patterns usually arise when simple patterns are transformed repetitively on smaller and smaller scales. An important difference between fractal curves and the normal curves that are normally applied to natural processes is that when dealing with fractals there are no distinct differences. That is, although they are continuous, they are looped everywhere. Fractals can be characterized by the way in which structure changes with their changing scale. One important class of processes that produce fractal patterns is random iteration algorithms, fractal, fractals, scale, patterns, objects, images, fractional, curve, way, structure, smaller, self-similarity, produce, processes, means, mandlebrot, important, image, idea, examples, every, data, curves, continuous, certain, applied, world, windows, whole, vessels, utilize, useless, understood, unchanged, trees, transmission, transition, transformed, tool, time, through, take, symbol, surface, stained, specifically, space, soon, simple, shrink