15.8. Fractals

A fractal is a geometric figure that can be generated from a pattern repeated recursively (Fig. 15.15). The figure is modified by applying the pattern to each segment of the original figure. We will look at a few such approximations in this section. [Note: We will refer to our geometric figures as fractals, even though they are approximations.] Although these figures had been studied before the 20th century, it was the Polish mathematician Benoit Mandelbrot who introduced the term “fractal” in the 1970s, along with the specifics of how a fractal is created and the practical applications of fractals. Mandelbrot’s fractal geometry provides mathematical models for many complex forms found in nature, such as mountains, clouds and ...

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