Preface Preface
This is an introductory text on the basics of chaotic dynamics and fractal geometry. The intended audience includes undergraduate students of mathematics or other technical disciplines with a strong background in calculus and some exposure (or willingness to explore) more advanced topics such as the basics of real analysis, the complex plane, and linear algebra.
Topics in the text include real iterative dynamics (experimentation, cobweb plots, bifurcation, and chaos), complex iterative dynamics (Julia sets, the Mandelbrot set, and the iteration of higher order polynomials), fractal geometry (self-similarity, iterated function systems and fractal dimension).
Another important aspect of this text is its emphasis on computation. We introduce Python code that runs live in the online version to generate images of many of the sets that we'll meet. Such code is generally quite simple using basic constructs such as function definition, conditionals, and iterative loops.
This text was written with PreTeXt which makes groovy things like live Python code and nicely formatted online and print versions easy.