# fractal

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Related to fractal: Fractal dimension

## fractal

[′frakt·əl]
(mathematics)
A geometrical shape whose structure is such that magnification by a given factor reproduces the original object.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## fractal

(mathematics, graphics)
A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a smaller copy of the whole. Fractals are generally self-similar (bits look like the whole) and independent of scale (they look similar, no matter how close you zoom in).

Many mathematical structures are fractals; e.g. Sierpinski triangle, Koch snowflake, Peano curve, Mandelbrot set and Lorenz attractor. Fractals also describe many real-world objects that do not have simple geometric shapes, such as clouds, mountains, turbulence, and coastlines.

Benoit Mandelbrot, the discoverer of the Mandelbrot set, coined the term "fractal" in 1975 from the Latin fractus or "to break". He defines a fractal as a set for which the Hausdorff Besicovich dimension strictly exceeds the topological dimension. However, he is not satisfied with this definition as it excludes sets one would consider fractals.

sci.fractals FAQ.

See also fractal compression, fractal dimension, Iterated Function System.

Usenet newsgroups: news:sci.fractals, news:alt.binaries.pictures.fractals, news:comp.graphics.

["The Fractal Geometry of Nature", Benoit Mandelbrot].

References in periodicals archive ?
The intention and suggestion of the Authors is to apply an innovation to the Black and Scholes method, basing the analysis of the pricing of the real options no longer on the normal distribution, but on a fractal approach.
In essence, with the implementation of the model suggested in this paper, it will be possible to replace the probability percentages assigned (currently by normal distribution) to each branch of the Black and Scholes construction, with more detail through the fractal approach.
According to (2), fractal dimension [D.sub.f] can be determined from the slope of the line of lgN(> r) and lg r in a log-log plot.
Then fractal dimension [D.sub.f] can be calculated from the lg [S.sub.Hg]-lg [p.sub.c] plot.
where [D.sub.f] and [[??].sub.f] are the fractal dimensions of the damage domain and the damage residual domain, respectively.
The recreation after effects of proposed fractal tree-shaped MSA is reviewed utilizing HFSS.
where d = 1 - D is the anomalous fractal dimension.
However, from the literature, these models have a shared problem that they are all based on MB fractal model.
To illustrate the fractal function of (1) for different values of fractal dimension D, some representative simulations of that are shown in Fig.
where M([epsilon]) means the length of a line, the area of a surface, the volume of a cube, or the weight of an object; D is the fractal dimension.

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