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A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ALL You Have Viewed Too Many Free Essays, Term Papers, and Book Reports. 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 Word Count: 429 Acceptance_Essays American_History Anatomy_&_Physiology Animal_Science_&_Zoology Anthropology Architecture Art Astronomy Aviation Biographies Book_Reports Business Computers Creative_Writing Current_Events Economics Education Engineering English Environmental_Science Ethics European_History Film_&_TV Foreign_Languages Geography Government_&_Politics Health_&_Beauty History_Other Human_Sexuality Legal_Issues Marketing Mathematics Medicine Miscellaneous Music Mythology Philosophy Physics Poetry Political_Science Psychology Religion Science Shakespeare Social_Issues Sociology Speech Sports_&_Recreation Supernatural Technology Theater Theses_&_Dissertations

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