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Fractals
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AbstractWe introduce a fractal as a mathematical object that has strong scaling behavior. That is, its “behavior” at one scale is strongly related to its “behavior” at finer scales. We give examples of many different types of geometric fractals and then introduce other types of fractal objects, like fractal functions or fractal random processes. These fractals can have exact scaling, approximate scaling, or only statistical scaling behavior. A particularly nice class of fractals are those defined by the iterated function system (IFS). We give an application of IFS fractals to image representation and close with some brief comments on a relationship between fractals and wavelets.
Title: Fractals
Description:
AbstractWe introduce a fractal as a mathematical object that has strong scaling behavior.
That is, its “behavior” at one scale is strongly related to its “behavior” at finer scales.
We give examples of many different types of geometric fractals and then introduce other types of fractal objects, like fractal functions or fractal random processes.
These fractals can have exact scaling, approximate scaling, or only statistical scaling behavior.
A particularly nice class of fractals are those defined by the iterated function system (IFS).
We give an application of IFS fractals to image representation and close with some brief comments on a relationship between fractals and wavelets.
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