Encounters with Chaos and Fractals

Encounters with Chaos and Fractals, Third Edition provides an accessible introduction to chaotic dynamics and fractal geometry. It incorporates important mathematical concepts and backs up the definitions and results with motivation, examples, and applications.The third edition updates this classic book for a modern audience. New applications on contemporary topics, like data science and mathematical modeling, appear throughout. Coding activities are transitioned to open-source programming languages, including Python.The text begins with examples of mathematical behavior exhibited by chaotic systems, first in one dimension and then in two and three dimensions. Focusing on fractal geometry, the authors introduce famous, infinitely complicated fractals. How to obtain computer renditions of them is explained. The book concludes with Julia sets and the Mandelbrot set.The Third Edition includes: More coding activities incorporated in each section with expanded code to include pseudo-code, with specific examples in MATLAB(R) (or its open-source cousin Octave) and Python Additional exercises--many updated--from previous editions Proof-writing exercises for a more theoretical course Revised sections to include historical context Short sections added to explain applied problems in developing mathematics This edition reveals how these ideas are continuing to be applied in the 21st century, while connecting to the long and winding history of dynamical systems. The primary focus is the beauty and diversity of these ideas. Offering more than enough material for a one-semester course, the authors show how these subjects continue to grow within mathematics and in many other disciplines.