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This book provides the reader with an elementary introduction to chaos and fractals, suitable for students with a background in elementary algebra, without assuming prior coursework in calculus or physics. It introduces the key phenomena of chaos - aperiodicity, sensitive dependence on initial conditions, bifurcations - via simple iterated functions. Fractals are introduced as self-similar geometric objects and analyzed with the self-similarity and box-counting dimensions. After a brief discussion of power laws, subsequent chapters explore Julia Sets and the Mandelbrot Set. The last part of the book examines two-dimensional dynamical systems, strange attractors, cellular automata, and chaotic differential equations. The book is richly illustrated and includes over 200 end-of-chapter exercises. A flexible format and a clear and succinct writing style make it a good choice for introductory courses in chaos and fractals. Contents Introducing Discrete Dynamical Systems Opening Remarks Functions Iterating Functions Qualitative Dynamics Time Series Plots Graphical Iteration Iterating Linear Functions Population Models Newton, Laplace, and Determinism Chaos Chaos and the Logistic Equation The Buttery Effect The Bifurcation Diagram Universality Statistical Stability of Chaos Determinism, Randomness, and Nonlinearity Fractals Introducing Fractals Dimensions Random Fractals The Box-Counting Dimension When do Averages exist? Power Laws and Long Tails Introducing Julia Sets Infinities, Big and Small Julia Sets and The Mandelbrot Set Introducing Julia Sets Complex Numbers Julia Sets for f(z) = z2 + c The Mandelbrot Set Higher-Dimensional Systems Two-Dimensional Discrete Dynamical Systems Cellular Automata Introduction to Differential Equations One-Dimensional Differential Equations Two-Dimensional Differential Equations Chaotic Differential Equations and Strange Attractors Conclusion Appendices