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Fractals Cover





If the eye attempts to follow the flight of a gaudy butterfly, it is arrested by some strange tree or fruit; if watching an insect, one forgets it in the strange flower it is crawling over; if turning to admire the splendour of the scenery, the individual character of the foreground fixes the attention. The mind is a chaos of delight...

Charles Darwin,

writing home from his Beagle voyage on his impressions of the Brazilian tropical rain forest.

Hike into a forest and you are surrounded by fractals. The inexhaustible detail of the living world (with its worlds within worlds) provides inspiration for photographers, painters, and seekers of spiritual solace: the rugged whorls of bark, the recurring branching of trees, the erratic path of a rabbit bursting from underfoot into the brush, and the fractal pattern in the cacophonous call of peepers on a spring night.

The landscape is the crucible in which living forms have evolved, and since the landscape crackles with fractals, the forms bred there are fractal as well. Living creatures, from trees to beetles to whales, have shapes and behaviors that provide a fractal record of the dynamical forces (the endless feedback) that act upon them and within them, forces that have continually caused them to evolve new niches in which to live. In his Boston Globe newspaper column, physicist and science writer Chet Raymo declared after seeing a museum exhibition of beetles, "Darwinian explanations are reasonable enough, but...the spectacular variability of beetles suggests that nature is infected by...a sheer lunatic exuberance for diversity, a manic propensity to try any damn thing that looks good or works."

The riotous beauty and dreamlike strangeness of nature provided a chief inspiration for Charles Darwin as he struggled to develop a coherent theory of evolution. Psychologist Howard Gruber, who has done a lengthy study of how Darwin arrived at his theory, says, "The meaning of his whole creative life work is saturated with...duality....

On the one hand, he wanted to face squarely the entire panorama of changeful organic nature in its amazing variety, its numberless and beautiful contrivances, and its disturbing irregularity and imperfections. On the other hand, he was imbued with the spirit of Newtonian science and hoped to find in this shimmering network a few simple laws that might explain the whole movement of nature." Darwin concludes his landmark Origin of Species with a striking metaphor of nature as "the tangled bank," reveling in what Gruber calls "the spectacle of complexity itself." Indeed, the pattern — the image — that gave Darwin his essential insight into how evolution works was a classic fractal: He conceived of the evolving forms of nature as an irregularly branching tree.

Examining Darwin's notebooks, Gruber carefully tracked Darwin's creative process to the moment when this image emerged in his thought. Gruber initially expected Darwin's mental processes on evolution would be "fine, clean, direct," but soon found that they were "tortuous, tentative, enormously complex." Gruber realized that "Darwin's picture of nature as an irregularly branching tree attributed to nature some of the characteristics I saw in his thinking."

According to Gruber, after considerable mental bifurcation Darwin reached a point where he drew in his notebook three tree diagrams which captured his insight that all creatures are related to one another through a process of branching pushed forward by natural selection. Darwin had found a simple law that could explain life's breathtaking complexity.

Through the ages artists have been driven by a desire to capture life's simultaneous complexity and simplicity in a single image or work. Some artists have created simple images with hugely complex overtones; others have spun out complex images that imply a simple order beneath. Artistic "truth" seems to involve presentation of a dynamic balance between these two opposites. Darwin's admiration for complexity and his belief in the Newtonian model of simple natural laws brought him an important step toward the artist's aesthetic (sense of harmony and dissonance), but in the end the emphasis of evolutionary theory fell on the simplicity side of the equation — on scientific law. Many of the scientists of chaos (though certainly not all) now seem bent on readjusting the balance. Accordingly, they are proclaiming a new dynamic that emphasizes how complexity can be wrought from simple rules while at the same time revealing a challenging new perception that the laws of complexity will forever prevent the kind of simple predictability and control over nature implied by the clockwork Newtonian model of the world that Darwin had admired.

Using simple mathematical rules, chaologists can now model complex dynamical systems, formulating rules to mimic on a computer such natural phenomena as the flocking pattern of birds flying to a roosting spot and the growing branch and leaf forms of specific flowers and trees. Chaos theory and fractal geometry have opened up undreamed of correspondences between the abstract mental realm of mathematics and the movements and shapes of our planet's myriad organisms. The seemingly endless niches in nature, for example, can now be perceived as an analogue for the intricate complexity which fractal geometers have found in the nooks and crannies of the Mandelbrot set. Indeed, the idea of niche itself can now be understood as a fractal idea.

Niche means a corner or space. Biologists have traditionally used the word to signify the little empty corner of an ecosystem that an organism evolves to fill; a niche presents an opportunity for evolution. If one species of cormorant nests on high cliffs with broad ledges and eats a certain kind of diet, another species will evolve with special characteristics that allow it to nest lower down on narrow ledges and eat a slightly different diet — so the two species occupy different niches. In this traditional view, nature abhors a vacuum and will evolve new forms to fill it. But, in fact, the situation is considerably more subtle. An organism creates the niche it occupies as much as it is created by the existence of an unexploited region of the ecosystem. New spaces or niches constantly come into being, unfolded by the total activity of organisms. When a species dies out, the fold (or niche) smooths over or is further crumpled into other folds. The great biological diversity on the planet is a sign that nature is continually rippling with new and related niches. It is like the surface of the sea wrinkling in the wind.

The constant crumpling of reality that we see in evolution takes place over millennia as species emerge and pass away, creating new landscapes, new environments, and new opportunities for new species. The old scientific concept of the "balance of nature" is quietly being replaced by a new concept of the dynamic, creative, and marvelously diversified "chaos of nature."

Copyright © 1992 by John Briggs

Product Details

Briggs, John
New York :
General science
Topology - Fractals
General Science
Edition Description:
Publication Date:
Grade Level:
178 4/C,29 B/W FOTOS;49 LINE
10 x 12 in 35.245 oz

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Fractals Used Trade Paper
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Product details 192 pages Touchstone Books - English 9780671742171 Reviews:
"Synopsis" by , Scientists have discovered that systems in transitional states between order and chaos possess certain patterns with unique, predictable qualities. These patterns are called "fractals". In essence, they are visual images or pictures of chaos at work. Now comes a breathtaking visual tour of this exciting new scientific frontier. 207 photographs, 178 in full color; 49 line drawings.
"Synopsis" by , Fractals are unique patterns left behind by the unpredictable movements — the chaos — of the world at work. The branching patterns of trees, the veins in a hand, water twisting out of a running tap — all of these are fractals. Learn to recognize them and you will never again see things in quite the same way.

Fractals permeate our lives, appearing in places as tiny as the surface of a virus and as majestic as the Grand Canyon. From ancient tribal peoples to modern painters to the animators of Star Wars, artists have been captivated by fractals and have utilized them in their work. Computer buffs are wild about fractals as well, for they can be generated on ordinary home computers.

In Fractals: The Patterns of Chaos, science writer John Briggs uses over 170 illustrations to clearly explain the significance — and more importantly, the beauty — of fractals. He describes how fractals were discovered, how they are formed, and the unique properties different fractals share. Fractals is a breathtaking guided tour of a brand new aesthetic of art, science, and nature. It will revolutionize the way you see the world and your place within it.

* Contains a special bibliography listing fractal generating software for desktop computers

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