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What are Fractals?

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Clouds are not spheres, mountains are not cones,
coastlines are not circles and bark is not smooth,
nor does lightning travel in a straight line.
- Benoit Mandelbrot

What is a fractal? (precisely)

It's hard to be precise! Like a biologists definition of life, a single definition doesn't capture all the important qualities.

It's a new word (c. 1975) and even those who know the word may have a hard time explaining it.

Which word does fractal sound like, or look like?

Fractals provides a way to quantify the roughness of a surface and generally have:

* detailed structure
* self-similarity in some sense
* simple formula, usually recursive
http://www2.cs.uregina.ca/~hepting/research/web/math-of-art/fractals.html

Word of caution: Mathematical fractals have geometrical and mathematical properties, they do not provide much information about the physics of the object, its origin or its physical properties. In addition, strictly mathematical fractals are not found in nature; they are just convenient models of some natural objects. Fractals become better models of natural objects when some randomness is included in their construction, for instance by slightly changing the rule at randomly selected iterations. Another important point, already mentioned above, but impossible to overemphasize, is that natural objects are self-similar only over a limited range of scales, and thus fractals can be used as models of nature only within a certain range of scales.
http://www.unc.edu/~myang/nonlinear/fractals/geometry.html

A fractal (from the Latin fractus, derived from the verb frangere, to break, to divide infinitely) is an object or a geometrical construct (or set of such objects) whose parts are somewhat identical or statistically similar with the whole through transformations that include translations, rotations and zooming. A structure is fractal if its finer shapes are indistinguishable or statistically similar to coarser ones, and thence there is no dominating scale.
http://www.unc.edu/~myang/nonlinear/fractals/defs.html

 

For more information on fractals see below:

Atlas of the Mandelbrot set

M. Romera
Instituto de Física Aplicada
Consejo Superior de Investigaciones Científicas
Serrano 144, 28006 Madrid, Spain

link added January 20, 2006

http://sprott.physics.wisc.edu/sa.htm
Link added July 11, 2006

The edge of the Mandelbrot Set is infinitely complex and contains an infinite number of tiny Mandelbrots, each of which contains an infinite number of other tiny Mandelbrots.

References:

Benoit B. Mandelbrot (1983). The fractal geometry of nature. New York: W. H. Freeman.

http://innopac.ballarat.edu.au/search/i0387972722

APA citation:
Russell, R. (2008, October 29, 02:43 am). What are fractals?
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