The term fractal was coined by French mathematician Benoît Mandelbrot in 1975. He based the term on the Latin word fractus, which means broken. A fractal is a geometric figure with some special properties—it is irregular, fractured, or fragmented in appearance, and it is self-similar; that is, the figure looks much the same no matter how far away or how close up it is viewed. In addition, unlike most geometric shapes, fractals have infinite areas and perimeters.
Fractals can be found extensively in nature: clouds, trees, coastlines, and mountains can all be described as fractals. Because of this, fractal geometry has many practical applications. Geologists can model the meandering paths of rivers and the rock formations of mountains. Botanists can model the branching patterns of trees and shrubs. Astronomers can model the distribution of mass in the universe. Physiologists can model the human circulatory system. Physicists and engineers can model turbulence in fluids.
Fractal images are constructed by the iteration of a mathematical function, by repeatedly substituting certain geometric shapes with other shapes, or by repeatedly applying geometric transformations, such as rotation or reflection, to points. The results of the functions are then plotted on a graph, and the points are colored using a formula. (Mandelbrots famous fractal set is constructed by the recursive iteration of the formula z = z2 + c, where z and c are complex numbers, and c is a constant.) Because of the complexity of these calculations, and the number of iterations required, fractals are usually generated on a computer.
