CHAPTER 10Dynamical Systems and Fractals

In this chapter we are going to learn how to draw beautiful pictures of fractals, strange sets with some pretty amazing properties. Fractals arise naturally in the study of dynamical systems so we’ll begin our discussion there. A dynamical system is simply a system that is changing as opposed to a static system. So everything from the solar system to the flow of blood in our arteries to the pendulum of a clock qualifies as a dynamical system. In order to approach the subject mathematically we usually focus on a single function, or a family of functions, and ask what happens if we repeatedly apply the same function over and over. This simple setup will lead us to Julia Sets as well as the famous Mandelbrot ...

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