Don's Art
Don's Fractal Art
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A fractal is a rough or fragmented geometric shape that can be subdivided in parts,
each of which is (at least approximately) a reduced-size copy of the whole.
Fractals are generally self-similar and independent of scale. ���
There are many mathematical structures that are fractals; e.g.
Sierpinski
triangle,
Koch
snowflake,
Peano
curve,
Mandelbrot
set, and
Lorenz
attractor.
���Beno�t B. Mandelbrot gives a mathematical definition of 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 some sets
that could be considered fractals. ���
According to Mandelbrot, who invented the term:
"I coined fractal from the Latin adjective fractus.
The corresponding Latin verb frangere
means �to break�: to create irregular fragments.
It is therefore sensible -�and how
appropriate for our needs!�- that, in addition to
�fragmented� (as in fraction or refraction),
fractus should also mean �irregular,� both
meanings being preserved in fragment."
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