Fractals Visualization and J [Paperback]

Clifford A. Reiter (Author)

Book Description

ISBN-10: 1895721180 | ISBN-13: 978-1895721188 | Publication Date: January 23, 2007 | Edition: 2nd

Fractals is a hands-on introduction to the visualization of mathematical objects, algorithms and data. The book gives a self-contained introduction to J as raster and object graphics are introduced. Fractal times series illustrate techniques for dealing with one-dimensional data. Studies of iterated function systems and chaotic attractors offer experience with visualizing two dimensional phenomena while investigating fractals and symmetry. Finite automata and fast Fourier transforms are used for playful things like the game of life and serious topics such as image processing. Similar techniques are used for studying classical complex dynamics illustrated by the Mandelbrot set and Julia sets. The mathematics of three dimensional projection is discussed and visualization of three dimensional data is the focus of scenes created by rendering J created objects with raytracers and OpenGL.

Editorial Reviews

About the Author

Cliff Reiter was born and grew up in central New Jersey. His doctoral thesis, done under the direction of Wen-Ching (Winnie) Li, concerned lower bounds on the fundamental units of real quadratic fields. Part of that work grew out of symbolic algebra computations that he programmed in APL. He continues to seek opportunities for application of computers to both research problems and teaching. He is enthusiastic about using high level programming languages for that work and has been quite successful at combining his teaching and research by engaging undergraduates in his research work. His research has continued in elementary number theory and has extended to topics in dynamics and mathematical visualization. He is the coauthor of a textbook APL with a Mathematical Accent and he is the author of the text Fractals, Visualization and J. He was the co-principal investigator for a National Science Foundation grant to build a Mathematica Laboratory used in teaching Calculus at Lafayette College and he was the principal investigator for a National Science Foundation Research Experiences for Undergraduates program at Lafayette College from 1992 to 1997. He has continued NSF supported work on chaos and crystallographic symmetry during the summers of 1998-1999.

Product Details

• Paperback: 375 pages
• Publisher: lulu.com; 2nd edition (January 23, 2007)
• Language: English
• ISBN-10: 1895721180
• ISBN-13: 978-1895721188
• Product Dimensions: 9.1 x 7.4 x 0.9 inches
• Shipping Weight: 1.8 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,927,723 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

7 of 7 people found the following review helpful:

5.0 out of 5 stars Excellent Book (By an Excellent Professor), June 12, 2002

By 

"lafrob" (Morgantown, Pennsylvania United States) - See all my reviews

This review is from: Fractals Visualization and J (Paperback)

As a Computer Science major, and also hobbyist, I've worked with Q-Basic, C++, Java, HTML, but never had I worked with a language like J. I had enrolled in Professor Reiter's course with a moderate interest in the language and a strong interest in the math. I ended a course with a strong interest in the math and a stronger interest in using the language. Where else can you use a few simple characters with such efficiency and power?
The key for my increase in interest in the language was the usage demonstrated in this book. It's amazing the mathematical techniques and areas that can be explored using J. I'm only just beginning my career at Lafayette College, but I've been presented with many upper level ideas to explore, both within J and without. In presenting the ideas, Reiter does assume some mathematical background, but not so much that it is daunting. Rather, the background is simply used to explain what you do with the language. Even if you don't understand the math, the book still allows you to implement the J code and return the result.
In essence, this book teaches a person how they can create math "art", all with the use of a powerful and robust language. I advise all interested in computer science to read this book and see how a seemingly obscure programming language can be used to explore some very interesting areas of mathematics.