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TOPIC: Fractals

Fractals 22 Sep 2014 19:27 #1

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Fractal

''A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale. If the replication is exactly the same at every scale, it is called a self-similar pattern.[1] Fractals can also be nearly the same at different levels. This latter pattern is illustrated in Figure 1.[2][3][4][5] Fractals also includes the idea of a detailed pattern that repeats itself.[2]:166; 18[3][6]

Fractals are different from other geometric figures because of the way in which
they scale. Doubling the edge lengths of a square scales its area by four, which is
two to the power of two, because a square is two-dimensional. Likewise, if the
radius of a sphere is doubled, its volume scales by eight, which is two to the
power of three, because a sphere is three-dimensional. If a fractal's one-dimensional
lengths are all doubled, the spatial content of the fractal scales by a power of two
that is not necessarily an integer.[2] This ratio is called the fractal dimension of the
fractal, and it usually exceeds the fractal's topological dimension.[7]''
en.wikipedia.org/wiki/Fractal

''A fractal is an object or quantity that displays self-similarity, in a somewhat technical
sense, on all scales. The object need not exhibit exactly the same structure at all
scales, but the same "type" of structures must appear on all scales. A plot of the
quantity on a log-log graph versus scale then gives a straight line, whose slope is
said to be the fractal dimension.''
mathworld.wolfram.com/Fractal.html

Fractals, at its inception, is based on pure mathematics. Now it has become widespread
and multidisciplinary, and its applications have evolved into many disciplines such
as physics, chemistry, earth and geological sciences, material sciences and engineering,
transport physics (fluid flow, heat transfer, electrical and wave transport) in porous
media, etc. It has been shown that whenever Fractals is applied to the multi-disciplines,
its unique worth can be unravelled and discovered repeatedly.''
www.worldscientific.com/worldscinet/fractals





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