ABSTRACT
This chapter discusses chaos in simple settings. Chaos occurs in elementary mathematical objects—objects as familiar as quadratic functions—when they are regarded as dynamical systems. The chapter explains simple mathematical operations like taking the square root, squaring, or cubing as dynamical systems by repeating the procedure over and over, using the output of the previous operation as the input for the next. This process is called iteration. This procedure generates a list of real or complex numbers that are changing. Dynamical systems have a long and distinguished history as a branch of mathematics. Beginning with the fundamental work of Isaac Newton, differential equations became the principal mathematical technique for describing processes that evolve continuously in time. The major development in dynamical systems was the availability of high-speed computing and, in particular, computer graphics.
