BOOK REVIEW - Computers, Pattern, Chaos and Beauty (by Clifford Pickover)
Citation: Technology Review, August-Sept 1990 v93 n6 p76(2)
Title: Computers, Pattern, Chaos and Beauty. (book reviews)
Authors: Sorenson, Peter
People: Pickover, Clifford A.
Rev Grade: B
Reference #: A9259759
Computers, Pattern, Chaos and Beauty
COMPUTER graphics has become indispensable in countless areas of human activity. The arts have been strongly affected by computer paint systems, synthesized special effects for motion pictures, and "3-D" television graphics, while industry has long used computer graphics in product design, engineering, and architecture. And from medicine to fluid dynamics, from atomic physics to astrophysics, there are nearly as many scientific applications of computer graphics as there are areas of study.
All this activity has spawned quite a number of books on digital imagery, most of which fall into one of two categories: those written for the layperson (which are full of glossy photos but generally short on meat), and textbooks for the programmer (which are largely indecipherable by anyone outside the field, and not likely to be illustrated very beautifully).
That's one reason Computers, Pattern, Chaos and Beauty, by Clifford A. Pickover, is so unusual. On the one hand, the scientist/artist author--an associate editor of Computer and Graphics magazine--eases the nonspecialist into this collection of essays by providing ample background information on computer graphics along with fascinating high-resolution images. On the other hand, he balances clarity with technical sophistication in accomplishing his main tasks: describing graphical methods for representing and detecting patterns in complicated data, and illustrating simple techniques for visualizing chaotic behavior. He augments this discussion with numerous "recipes" for recreating most of the graphics programs he has devised.
In researching ways to visualize information, Pickover eschews the usual scientific method, whereby a problem is precisely defined and then narrowly investigated. Instead he casts his hook wherever the waters seem most fertile. He hops from fractals and chaos to the shroud of Turin, music, acoustic waveforms, genetics, snowflakes, and much more. Often Pickover applies software he has developed for one field to others where most people might not think to use them. For example, he used tools designed for speech synthesis research to find new ways of depicting the sequence of ases in a cancer gene.
Pickover extends the concept of fractals--geometric shapes that repeat themselves on different scales--to encompass not just the seemingly chaotic systems like water and fire that they are known to underlie but also living organisms. His "biomorphs," a class of fractals he invented that look like primitive aquatic organisms, are an example. Pickover peers into these complex shapes as if they were drops of pond water under magnification.
The discovery of the biomorph creatures began with a bug in a program that Pickover and an associate had written to generate Mandelbrot sets--beautiful, infinitely complex fractal shapes created by the massive repetition of simple mathematical feedback loops. The bug caused triangular elements to appear everywhere in the fractal's pattern. By the time they had figured out what was wrong, the researchers were hooked by its unique aesthetics and went on to exploit it. Under their godlike control, the triangles evolved into tapered strands that remind one of the cilia, or tiny hairs, on microbes.
Biomorphs' uncanny resemblance to primitive organisms leads the author to wonder if fractals might lie at the root of the forms assumed by living things. He muses freely on where further work might lead:
"Like ancient ants trapped in amber, the biomorphs remind us of the fossils of primitive life. If such complicated shapes can be found in the fabric of mathematical space formed with relatively simple equations, we might wonder if even 'higher' forms could be found by searching spaces defined by more complicated equations."
In his quest for ways to represent complicated data, Pickover has developed the deceptively simple "symmetrized dot-pattern," or SDP. The author has discovered that the human eye/brain finds graphs of acoustic waveforms much easier to digest if they are turned into six-sided patterns of dots like those of a kaloidoscope. He displays digitized sounds--human voices, animal vocalizations, and the bearing of hearts in various states of health -- in circular graphs with the threefold symmetry of snowflakes. In this way, sonograms representing the same vowel pronounced by different people, as unique as fingerprints but equally confusing to the untrained eye, become flowerlike SDPs that are instantly recognizable. The author foresees a useful application for SDPs in medicine: applied to electrocardiograms, they could make heart abnormalities easier to detect.
Many of Pickover's projects combine scientific investigation with aesthetic pleasure. His tessellation patterns are an example. Starting with a simple figure such as a triangle or squiggle, he applies repeating rules to make the figure reproduce itself automatically in complex patterns. In the process he not only demonstrates a kind of simplified ecology-on-a-computer--representing organic growth and life cycles--but generates exquisite mosaics.
Beyond its obvious contributions to research in a variety of fields, Computers, Pattern, Chaos and Beauty will awaken a wide audience to the astounding visual beauty hidden in methematics and science.
PETER SORENSEN is a computer graphics consultant based in Santa Monica, Calif.
Full Text COPYRIGHT Massachusetts Institute of Technology Alumni Association