A New Kind of Science1 is Stephen Wolfram's magnum opus on cellular automata, and the main reason why he hasn't published many works in the past few years. This book covers almost all of the work done in the cellular automata field written with an easily readable style in order to be accessible for those not so well versed in the subject. It also has an amazing set of notes following the main text, delving into much more detail for those so inclined.
This book, although written in Wolfram's trademark egotistical style, lays important groundwork in for describing nature and computational processes using very simple cellular automata (Wolfram even goes so far as to state that the Universe can probably be condensed into a few lines of Mathematica code). The introductory chapters introduce the reader to the rich world of cellular automata, replacement systems, and turing machines. Here, Wolfram also introduces his intention that this new kind of science replace the aging logical system which we call Mathematics, at least as a description language for the structure and function of natural systems. He talks about the similarities between cellular automata and the universe and gives very eloquent reasoning as to why cellular automata are a good model for exploring a wide range of natural systems.
The last few chapters of the book are concerned with his Principle of Computational Equivalence, which states "almost all processes that are not obviously simple can be viewed as computations of equivalent sophistication." Basically, natural systems can be viewed as performing computation, and this computation is equally as powerful as that performed by Turing Machines, the human brain, or the universe itself. This also implies that no system build within the constraints of the universe can compute with more power than the universe. It will be interesting to watch this field in the next few years to see what kind of effect this book will have.
Table of Contents
- The Foundations for a New Kind of Science
- The Crucial Experiment
- The World of Simple Programs
- Systems Based on Numbers
- Two Dimensions and Beyond
- Starting from Randomness
- Mechanisms in Programs and Nature
- Implications for Everyday Systems
- Fundamental Physics
- Processes of Perception and Analysis
- The Notion of Computation
- The Principle of Computational Equivalence
The main text is about 800 pages long, followed by 300 more pages of notes in a much smaller font.
- Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, 2002. ISBN 1-57955-008-8.