Chapter 8. Fractals


There are many aspects in nature that are repeating and many cases of patterns similar at different scales. For example, when observing a pine tree, one may notice that the shape of a branch is very similar to that of the entire tree, and the shapes of sub-branches and the main branch are also similar. Such kind of self-similar structure that occurs at different levels of magnification can be modeled by a branch of mathematics called Fractal geometry. The term fractal was coined by Benoît Mandelbrot in 1975, and means fractus or broken in Latin. Fractal geometry studies the properties and behavior of fractals. It describes many situations which cannot be explained easily by classical geometry. Fractals can be used to model plants, weather, fluid flow, geologic activity, planetary orbits, human body rhythms, socioeconomic patterns, and music, just to name a few. They have been applied in science, technology, and computer generated art. For example, engineers use fractals to control fluid dynamics in order to reduce process size and energy use.

A fractal, typically expressed as curves, can be generated by a computer recursively or iteratively with a repeating pattern. Compared with human beings, computers are much better in processing long and repetitive information without complaint. Fractals are therefore particularly suitable for computer processing. This chapter introduces the basic concepts and program implementation of fractals. It starts with ...

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