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Library of Congress Cataloging-in-Publication Data

Wolfram, Stephen, 1959 –

A New Kind of Science / Stephen Wolfram.

p. cm

Includes index.

ISBN 1-57955-008-8 (alk. paper)

1. Cellular automata. 2. Computational complexity. I. Title.

QA267.5.C45 W67 2001

500—dc21 2001046603

CIP

distributed, transmitted, publicly performed or displayed without the prior written consent of the copyright holder. Nor may derivative works such

as translations be produced. Visit www.wolframscience.com/nks/permissions for further information.

The author, copyright holder and publisher wish to encourage further development of the science in this book, while maintaining its intellectual

integrity and preserving the value of their substantial creative and financial investments through the maintenance of appropriate legal and other rights.

Discoveries and ideas introduced in this book, whether presented at length or not, and the legal rights and goodwill associated with them, represent

valuable property of Stephen Wolfram,

LLC, and when they or work based on them is described or presented, whether for scholarly purposes or

otherwise, appropriate attribution should be given. For purposes of scholarly citation this book is a primary source, and should be cited accordingly.

Individual verbatim quotations of up to twenty lines of plain text may be made for scholarly purposes if this book is clearly identified and cited as the

source. Visit www.wolframscience.com/nks/reprints for information on classroom reprints and copying arrangements.

Illustrations (including tables) may not be reproduced without the prior written consent of the copyright holder. Most individual illustrations in this

book represent substantial original works in themselves, and their reproduction is not a fair use. Visit www.wolframscience.com/nks/images to request

permission to reproduce illustrations, and for information on high-resolution and electronic versions. Permission to reproduce illustrations will

normally be granted for scholarly purposes so long as the illustrations are not modified, are reproduced with satisfactory quality, are used and

explained in an appropriate way, have adjacent captions or text that clearly identifies this book as their source, and specify Stephen Wolfram,

LLC as

the holder of their copyright. Stephen Wolfram,

LLC is the owner of the full copyright to all illustrations in this book (except as indicated in the

colophon), including their form of presentation and such original elements as non-obvious choices of rules and initial conditions used to create them.

Scholarly discussion and development subject to restrictions of fair use is nevertheless encouraged.

This book contains many Mathematica programs in source code form. These represent licensed software and may be executed on any duly-licensed

Mathematica-compatible system. Their source code may be reproduced verbatim for non-commercial purposes so long as it is identified in each

instance as a Mathematica program and this book is cited as its source. Derivative works such as modified or translated versions may not be made

available without prior written consent of the copyright holder. Consent will normally be granted for non-commercial purposes so long as the original

version of each program is included, together with appropriate copyright and other notices. Visit www.wolframscience.com/nks/programs for

downloadable programs, and for fur ther licensing information. The Mathematica system and language is copyrighted by Wolfram Research, Inc.

Certain material in this book may be proprietary, and may for example be or become the subject of U.S. or foreign patents, pending or issued.

Inclusion in this book shall not be construed as implying any license of any sort. Visit www.wolframscience.com/nks/licensing for licensing information.

There are no warranties, express or implied, made with respect to programs, specifications, models, instructions or information contained in this book.