## Cellular Automata Machines: A New Environment for ModelingRecently, cellular automata machines with the size, speed, and flexibility for general experimentation at a moderate cost have become available to the scientific community. These machines provide a laboratory in which the ideas presented in this book can be tested and applied to the synthesis of a great variety of systems. Computer scientists and researchers interested in modeling and simulation as well as other scientists who do mathematical modeling will find this introduction to cellular automata and cellular automata machines (CAM) both useful and timely.Cellular automata are the computer scientist's counterpart to the physicist's concept of 'field' They provide natural models for many investigations in physics, combinatorial mathematics, and computer science that deal with systems extended in space and evolving in time according to local laws. A cellular automata machine is a computer optimized for the simulation of cellular automata. Its dedicated architecture allows it to run thousands of times faster than a general-purpose computer of comparable cost programmed to do the same task. In practical terms this permits intensive interactive experimentation and opens up new fields of research in distributed dynamics, including practical applications involving parallel computation and image processing.Contents: Introduction. Cellular Automata. The CAM Environment. A Live Demo. The Rules of the Game. Our First rules. Second-order Dynamics. The Laboratory. Neighbors and Neighborhood. Running. Particle Motion. The Margolus Neighborhood. Noisy Neighbors. Display and Analysis. Physical Modeling. Reversibility. Computing Machinery. Hydrodynamics. Statistical Mechanics. Other Applications. Imaging Processing. Rotations. Pattern Recognition. Multiple CAMS. Perspectives and Conclusions.Tommaso Toffoli and Norman Margolus are researchers at the Laboratory for Computer Science at MIT. Cellular Automata Machines is included in the Scientific Computation Series, edited by Dennis Cannon. |

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### Contents

Cellular automata | 5 |

The CAM environment | 13 |

A live demo | 19 |

The rules of the game | 27 |

Our first rules | 37 |

Secondorder dynamics | 47 |

Neighbors and neighborhoods | 55 |

Randomness and probabilistic rules | 67 |

The Margolus neighborhood | 119 |

Symptoms vs causes | 141 |

Diffusion and equilibrium | 155 |

Fluid dynamics | 171 |

Collective phenomena | 185 |

Ballistic computation | 209 |

Conclusions | 221 |

B Basic CAM architecture | 243 |

A sampler of techniques | 77 |

Identity and motion | 101 |

Pseudoneighbors | 109 |

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255 | |