Graphics with Mathematica

Fractals, Julia Sets, Patterns and Natural Forms

Chonat Getz, Janet Margaret Helmstedt

• Publisher: Elsevier Science
• Year: 2004
• Print ISBN:
  9780444517609
• eBook ISBN:
  9780080472874
• Topic: Mathematics
• Subtopic: Discrete Mathematics
• Index: Mathematics

In this book we generate graphic images using the software Mathematica thus providing a gentle and enjoyable introduction to this rather technical software and its graphic capabilities. The programs we use for generating these graphics are easily adaptable to many variations.These graphic images are enhanced by introducing a variety of different coloring techniques.Detailed instructions are given for the construction of some interesting 2D and 3D fractals using iterated functions systems as well as the construction of many different types of Julia sets and parameter sets such as the Mandelbrot set.The mathematics underlying the theory of Iterated function systems and Julia sets is given an intuitive explanation, and references are provided for more detailed study.·Brilliant Graphic images·Interesting Introduction to Mathematica for Beginners·Easy constructions ·A variety of Coloring Techniques·Programs Easily Adaptable to Many Variations·Constructions useful for Dynamics and Fractals Courses

Table of contents

• Cover
• Preface
• Acknowledgements
• Contents
• Basics
• Using Color in Graphics
• Patterns Constructed from Straight Lines
• Orbits of Points Under a Nsub->Nsub Mapping
• Using Roman Maeder's Packages AffineMaps, Iterated Function Systems and Chaos Game to Construct Affine Fractals
• Constructing Non-Affine and 3D Fractals Using the Deterministic and Random Algorithms
• Constructing Julia and Mandelbrot Sets with the Escape-Time Algorithm and Boundary Scanning Method
• Miscellaneous Design Ideas
• Appendices
• Bibliography
• Index