Chaos: Making a New Science
A great book, one of the best books I have ever read! I just can't stop plugging it! Explains the history and development of chaos theory from its very birth to fairly recent times. Includes great pictures, diagrams, explanations, and some great color plates. James Gleick is an excellent science writer whose prose neither alienates laypeople nor bores experts. Chaos was truly one of the most revolutionary books covering chaos science. Highly, highly recommended as a great introductory text on chaos theory.
The Fractal Geometry of Nature
Benoit B. Mandelbrot
Everybody knows Benoit Mandelbrot (except maybe primitive aborigine basket-weavers who have lived inside paper bags in Antarctica all their lives and are deaf, dumb, blind, and danged stupid) of IBM; he discovered the fascinating Mandelbrot set generated by repeated iteration of a simple recursive function operating on the complex number space. The vaguely pear-shaped resultant image plotted on the Argand plane has provided some of the most fascinating images ever created. This book discusses, in a more general than scientific vein, most everything Mandelbrot eventually associated with fractals. Fairly old but makes good reading; esoterically confusing mathematical discussions are balanced by some great three-dimensional fractal pictures including the famous Planetrise and a killer conception of a Sierpinski pyramid.
An Eye For Fractals: A Graphic & Photographic Essay
A good beginning book on fractals; excellent low-level lay text very suitable for those as yet unfamiliar with chaos theory. The author attempts to make a statement about fractals and their relationships with nature; fractals are shown juxtaposed with strikingly beautiful photographs of landscapes, trees, rocks, and other Ansel Adams reminiscent natural phenomena displaying a fractal nature. Contains one of the best explanations of fractal dimension for beginners available. Mandelbrot and Julia sets are covered well. The author also unsuccessfully attempts to explain affine transformations. Valuable mainly as a compendium of pretty pictures.
The Beauty of Fractals: Images of Complex Dynamical Systems
Heinz-Otto Peitgen/Peter H. Richter
The two authors of this spectacular work are truly giants in the fractal image industry. This book is widely recognzied as the source of some of the most spectacular pictures of fractals to be found anywhere, with the possible exception of the various prolific fractal movies produced almost daily from Caltech. Very good book with highly esoterical mathematics balanced with incredible fractal graphics.
The Science of Fractal Images
Heinz-Otto Peitgen/Dietmar Saupe (Editors)
Michael F. Barnsley / R.L Devaney / Benoit B. Mandelbrot / Heinz-Otto Peitgen / Dietmar Saupe / Richard Voss (Contributors)
The names in this title cause involuntary genuflection. All the big giants of the infant fractal arena come out en masse and ready to tangle with any skeptic with this incredible book. Although the mathematics level is high-level (knowledge of advanced calculus and differential equations required except for one simple chapter), the pictures, particularly fractal landscapes and clouds, are truly breathtaking. Well, well, well worth reading and studying. Breakthrough, FAST algorithms for calculating the Mandelbrot set, great IFS methods, and other such neat stuff.
Fractal Geometry: Mathematical Foundations and Applications
A handy little tome filled with lots of math jargon and useless proofs. For the layman, useful only for the sections concerning random variations of regular fractals which produce wonderful results. Concerns itself more with the advanced mathematics driving chaos than with the applications on either computers or physical sciences.
Michael F. Barnsley
The King of Iterated Function Systems, Michael F. Barnsley, makes his presence felt with this textbook devoted almost entirely to the IFS method, Collage Theorem, and other brainchilds leading to image compression which produce very nice images. Has good listings of transformations for homebrew programmers to churn up in their computers, as well as examples of stunningly detailed pictures purely generated by the IFS method.
Chance and Chaos
A mathematical book concentrating more on probability than chaos theory. Vaguely interesting, but a bit dry for anybody for whom mathematics is not completely enjoyable--but what can you expect from a professor of theoretical physics? Has an interesting section on the Lorenz attractor. The author was one of the original researchers studying the Lorenz attractor and thus was an important Founding Father of chaos theory; sadly, he today bemoans the state of chaos theory and declares that it has discovered nothing truly real. It is, I suppose, up to us to decide and hopefully disprove.
Fractals: Endlessly Repeated Geometrical Figures
A good book that explains much concerning fractals; listings of many extremely poor-quality, but functional, programs in Turbo Basic. Some great explanations of chaotic orbits and asthetic chaos. The main usefulness of this book lies in its listings of the ranges and values that provide good orbits, and the explanations of basic fractal construction. Contains a few very good line-replacing method fractal generators which produce great fractal curves, albeit not quite as efficiently as with the more recent L-system method.
A Geometry of Nature
Computer-oriented only in that it contains program listings, this mostly practical book contains a treasure trove of differential equations and recursive functions suitable for programmers. Ignore the programs themselves, inefficient dinosaurs written in Turbo Basic; they all plot points to a file, and then read these points, a horribly noninteractive and unentertaining process which takes away the fun of watching a strange attractor fly across a computer screen. The equations and algorithms listed here, however, are extremely useful.
Does God Play Dice? (The Mathematics of Chaos)
An interesting book which covers nearly everything about chaos theory without going in-depth on any of its aspects. No algorithms are provided except the well-known IFS algorithm of the Sierpinski triangle, but there are some good diagrams and pictures and a good section on the easy-to-perform water drop experiment which may be of interest to airchair researchers.
Artificial Life: The Quest for a New Creation
Authored by one who has been around since the early days of the MIT labs, who watched "Slug" Russell program the original "Spacewar," this book explains cellular automata such as Life and other systems in great detail and postulates on possible artificial life arising from these. A truly fascinating story of an engrossing field, with good background information on everything covered. This is definitely a book well worth reading for background on complexity and the idea that order arising from disorder is in fact a natural process. Great explanations of cellular automata from one-dimensional Wolfram systems to the John Conway Life conception and the Langton eight-state self-replicating pattern.
Included mainly for inspirational value; this book is the monumental story of the early days of computer hacking. Great anecdotes and history of the MIT computer labs gives insight into that strange breed we call computer programmers. As a flimsy excuse for being plugged in this chaos theory related bibliography, this book does have a section on obsessed hackers madly scrambling on Life, both on computers and with actual checkerboards.