Fractal

Fractal is a complex geometric shape that can be split into parts, each of which is a reduced-scale copy of the whole. Fractals are used in computer modeling of natural structures that are not easily described by classic geometry, such as clouds, mountain ranges, lightning bolts, coastlines, and trees.

Definition

A fractal is a mathematical set that exhibits a repeating pattern that displays at every scale. It is also known as expanding symmetry or evolving symmetry. If the replication is exactly the same at every scale, it is called a self-similar pattern.

History

The term fractal was first used by mathematician Benoit Mandelbrot in 1975. Mandelbrot based it on the Latin fractus, meaning "broken" or "fractured", and used it to extend the concept of theoretical fractional dimensions to geometric patterns in nature.

Characteristics

Fractals are characterized by fine structures at arbitrarily small scales, and by being too irregular to be easily described in traditional Euclidean geometric language. For images of fractal patterns, this has been expressed by phrases such as "smoothly piling up surfaces" and "swirls upon swirls".

Applications

Fractals have been employed in various fields such as computer graphics, physical sciences, and network theory. They are also found in nature and have been used to model natural phenomena.

See also

• Mandelbrot set
• Julia set
• Fractal dimension
• Fractal landscape

References

Fractal Resources
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