A fractal is a rough or fragmented geometric shape that can be subdivided in parts. Each part is approximately a reduced-size copy of the whole. The term fractal was first used by Benoît Mandelbrot in 1975. It is derived from the Latin fractus meaning “broken” or “fractured”. A fractal as a geometric object generally has the following characateristics:
A fractal has a fine structure at arbitrarily small scales. A fractal is too irregular to be easily described in traditional Euclidean geometric language. A fractal is self-similar. A fractal has a Hausdorff dimension which is greater than its topological dimension. A fractal has a simple and recursive definition. Because fractals appear similar at all levels of magnification, they are often considered to be infinitely complex. There are natural objects that approximate fractals. Some of these include clouds, mountain ranges, lightning bolts, coastlines and snow flakes. However, not all self-similar objects are fractals—for example, the real line is formally self-similar but fails to have other fractal characteristics.
