Fractals


Geometrical entities characterized by basic patterns that are repeated at ever decreasing sizes. For example, trees describe an approximate fractal pattern, as the trunk divides into branches which further subdivide into smaller branches which ultimately subdivide into twigs; at each stage of division the pattern is a smaller version of the original.

Fractals are not able to fill spaces, and hence are described as having fractional dimensions. They were devised in 1967 by Benoit Mandelbrot, during a study of the length of the coastline of Britain. They are relevant to any system involving self-similarity repeated on diminishing scales, such as in the study of chaos, fork ligihtning, or the movement of oil through porous rock. They are also used in computer graphics.

The most famous fractal is the Mandelbrot set, the set of complex numbers that describes the behaviour of points z under the iterative process f(z) = z2 +c for different values of c. Its fractal nature illustrates the sensitive way in which iterations depend on the choice of c. It also occurs in other iterative processes.

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