Computers and the Imagination: Visual Adventures Beyond the Edge

455 Pages·1991·68.54 MB·English

by  Clifford A. Pickover

Computers and the
Imagination
Visual Adventures Beyond
the Edge
Clifford A. Pickover
ALAN SUTTON
ALAN SUTTON PUBLISHING
PHOENIX MILL • FAR THRUPP • STROUD
GLOUCESTERSHIRE • GL4 2BU
First published in the United Kingdom 1991
Copyright © Clifford A. Pickover 1991
All rights reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted, in any
form or by any means, electronic, mechanical, photocopying,
recording or otherwise, without the prior permission of the
publishers and copyright holder.
British Library Cataloguing in Publication Data
Pickover, Clifford A.
Computers and the imagination.
I. Title
006.6
ISBN 0 86299 999 5
To Elahe

Preface
The Buddha, the Godhead, resides quite as comfortably in the circuits of a
digital computer or the gears of a cycle transmission as he does at the top of
a mountain or in the petals of a flower; to think otherwise is to demean the
Buddha — which is to demean oneself Robert Pirsig, 1975
This book is meant to be a stimulus for the imagination - an energizing elixir for
scientific creativity. This book is also about some of the many things which
researchers do with a computer: simulating, visualizing, speculating, inventing,
and exploring. However, if a researcher’s primary investigative effort is consid­
ered as the trunk of a tree, then many of this book’s topics are the offshoots,
branches, and tendrils. Some of the topics in the book may appear to be curios­
ities, with little practical application or purpose. However, I have found all of
these experiments to be useful and educational, as have the many students, educa­
tors, and scientists who have written to me during the last few years. It is also
important to keep in mind that throughout history, experiments, ideas and conclu­
sions originating in the play of the mind have found striking and unexpected prac­
tical applications. I urge you to explore all of the topics in this book with this
principle in mind.
Computers and the Imagination will appeal to the educated layperson with a
curious or artistic streak, as well as students and professionals in the sciences, par­
ticularly computer science. Some of the patterns in this book can be used by
graphic artists, illustrators, and craftspeople in search of visually intriguing
designs, or by anyone fascinated by optically provocative art. The book is not
intended for mathematicians looking for a formal mathematical treatise. As my
previous book, Computers, Pattern, Chaos, and Beauty (St. Martin’s Press,
1990), the purposes of this book are:
1. to present several novel graphical ways of representing complicated data,
2. to promote and show the role of aesthetics in mathematics and to suggest how
computer graphics gives an appreciation of the complexity and beauty under­
lying apparently simple processes,
3. to show the beauty, the adventure, and the potential importance of creative
thinking using computers, and
4. to encourage the use of the computer as an instrument for simulation and dis­
covery.
“Lateral thinking” has been employed in the development of many of the
topics of this book. This is a term discussed by writer/philosopher Robert Pirsig
(author of Zen and the Art of Motorcycle Maintenance). As he explains it,
lateral thinking is reasoning in a direction not naturally pointed to by a scientific
discipline. It is reasoning in an unexpected direction, given the actual goal one is
working toward (also see de Bono, 1975). In this book, the term “lateral
thinking” is used in an extended way, and indicates not only action motivated by
unexpected results, but also the deliberate shift of thinking in new directions to
discover what can be learned.
Imagery is at the heart of much of the work described in this book. To under­
stand what is around us, we need eyes to see it. Computers with graphics capa­
bility can be used to produce visual representations from myriad perspectives. In
the same spirit as Martin Gardner’s book Mathematical Circus or Theoni
Pappas’ book The Joy of Mathematics, Computers and the Imagination com­
bines old and new ideas - with emphasis on the fun that the true scientific exp­
lorer finds in doing, rather than in reading about the doing.
This book is a collection of some of my papers published since Computers,
Pattern, Chaos, and Beauty. With just a few exceptions, all of the described
research and computer graphics in the book are my own. However, the Introduc­
tion and various one-page Interlude sections describe some unusual work by other
researchers in related fields. The Interlude sections and some of the appendices
also contain further information, images, and futuristic products to stimulate the
imagination.1
Computers and the Imagination includes topics such as scientific visualiza­
tion, simulation, number theory, and computer art, and you will be urged to
explore in greater depth the ideas presented. You should be forewarned that
some of the material presented involves sophisticated concepts (e.g. “Irregularly
Oscillating Fossil Seashell”); other chapters (e.g. “The Cancer Game”) require
little mathematical knowledge in order to appreciate the subject. You are encour­
aged to pick and chose from the smorgasbord of topics. Many of the articles are
brief and give you just a flavor of an application or method. Often, additional
information can be found in the referenced publications. In order to encourage
your involvement, computational hints and recipes for producing some of the com­
puter-drawn figures are provided. For many of you, seeing pseudocode will
clarify concepts in ways mere words cannot.
' Note: Although all of the products listed in this book provide a stimulus for the imagination, they are
listed for illustrative purposes only. The author does not endorse any particular software or
product, nor does he accept responsibility for the selection of any products by the reader. The opin­
ions expressed in this book are the author’s and do not represent the opinions of any organization or
company.
The book is organized into nine main sections:
1. Simulation. In the quest for understanding natural phenomena, we turn to
several simple computer simulations. These experiments are the easiest in the
book for students to implement and explore, and include butterfly curves and
cancer growth simulations.
2. Exploration. In this section, the interesting weave of “mathematical fabric”
is explored. Topics include the Lute of Pythagoras, earthworm algebra,
number theory, super-large numbers, and the elusive cakemorphic integers.
3. Visualization. Computer graphics has become indispensable in countless
areas of human activity. Presented here are experiments using graphics in
biology, mathematics, and art. Topics include pain-inducing patterns, sea-
shells, and voltage sculptures.
4. Speculation. In this section are several speculative survey articles. Topics
include “Who are the ten most influential scientists in history?” and “What is
the social and political impact of a soda-can-sized supercomputer?”
5. Invention. This section describes several inventions. Topics include anti-dys­
lexic fonts and speech synthesis grenades.
6. Imagination. Discussed here are computer-generated poetry and stories.
7. Fiction. Presented in this section are a few short stories dealing with com­
puters and scientific experiments.
8. Exercises for the Mind and Eye. This section presents imaginative unsolved
puzzles and curiosities. There are also serious experiments for future
research. Described in this section are Grasshopper sequences and the
Amazon skull game.
9. Computers in the Arts and Sciences. This last section treats you to a list of
unusual resources on the subject of computers in science and art. Listed are
individuals and companies distributing computer art, music, and films, and
also some references to unusual literature.
In deciding how to organize the material within these sections of Computers
and the Imagination, I considered a number of divisions - computer- and non-
computer-generated forms, science and art, nature and mathematics. However,
the lines between these categories become indistinct or artificial, and I have there­
fore arranged the topics randomly within each section to retain the playful spirit
of the book, and to give you unexpected pleasures. Throughout the book, there
are suggested exercises for future experiments and thought, and directed reading
lists. Some information is repeated so that each chapter contains sufficient back­
ground information, and you may therefore skip sections if desired. Smaller type
fonts, as well as the symbols [[ and ]], are used to delimit material which you can
skip during a casual reading, and a glossary is provided for some of the technical
terms used in the book.
At the beginning of many chapters of Computers and the Imagination are
large computer-generated “sculptures” constructed with tiny black dots. These
images are actually created from simple mathematical formulas, and each con­
tains precisely one-million dots. Background information, as well as algorithmic
recipes for these sculptures, can be found in “Million-Point Sculptures” on
page 285. Other frontispiece figures include grotesque Digital Monsters which
are discussed in “Descriptions of Color Plates and Frontispieces” on page 393.2
The basic philosophy of this book is that creative thinking and computing are
learned by experimenting. I conclude this preface with a quote from Morris Klein
0Scientific American, March 1955) that encompasses the general theme of this
book:
The creative act owes little to logic or reason. In their accounts of the cir­
cumstances under which big ideas occurred to them, mathematicians have
often mentioned that the inspiration had no relation to the work they hap­
pened to be doing. Sometimes it came while they were travelling, shaving, or
thinking about other matters. The creative process cannot be summoned at
will or even cajoled by sacrificial offering. Indeed it seems to occur most
readily when the mind is relaxed and the imagination roaming freely.
For Further Reading
1. De Bono, E. (1970) Lateral Thinking: Creativity Step by Step. Harper and
Row: New York.
2. Gardner, M. (1979) Mathematical Circus. Penguin: England. (A collection
of interesting puzzles, paradoxes, and games.)
3. Gardner, M. (1978) Aha! Insight. Freeman: New York. (A collection of
puzzles which encourages creative leaps of thought, leading to solutions of
seemingly impossible problems.)
4. Pappas, T. (1989) The Joy of Mathematics. Wide World Publishing: Cali­
fornia. (A collection of mathematical puzzles and concepts for the layperson.)
5. Pickover, C. (1990) Computers, Pattern, Chaos, and Beauty. St. Martin’s
Press: New York.
6. Pirsig, R. (1975) Zen and the Art of Motorcycle Maintenance. Bantam: New
York. (A philosophical story dealing with humans and technology.)
- Book cover. The cover of this book shows an image of a creature which the author rendered using an
IBM RISC System/6000 computer. Many aspects of the figure, including color, lighting, and
shading, are controlled by a computer program. The creature’s body was created using formulas
which produce three oscillating spiral shapes. The intricate background and diffuse collection of
tiny spheres toward the back of the figure were also generated by simple formulas. Information on
other color plates can be found in “Descriptions of Color Plates and Frontispieces” on page 393.
'Thinking is more interesting than knowing,
but less interesting than looking
Wolfgang von Goethe