By Larry S. Liebovitch

Fractals and chaos are at present producing pleasure throughout numerous clinical and scientific disciplines. Biomedical investigators, graduate scholars, and undergraduates have gotten more and more attracted to employing fractals and chaos (nonlinear dynamics) to numerous difficulties in biology and drugs. This available textual content lucidly explains those techniques and illustrates their makes use of with examples from biomedical learn. the writer provides the cloth in a truly precise, elementary demeanour which avoids technical jargon and doesn't imagine a powerful history in arithmetic. The textual content makes use of a step by step strategy by means of explaining one proposal at a time in a suite of dealing with pages, with textual content at the left web page and pix at the correct web page; the portraits pages might be copied without delay onto transparencies for educating. excellent for classes in biostatistics, fractals, mathematical modeling of organic platforms, and similar classes in medication, biology, and utilized arithmetic, Fractals and Chaos Simplified for the existence Sciences also will function an invaluable source for scientists in biomedicine, physics, chemistry, and engineering.

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As a scientist, Mandelbrot’s fame rests on his founding of fractal geometry, and on his showing how it applies in many fields. A fractal, a term he coined from the Latin for “broken,” is a geometric shape that can be broken into smaller parts, each a small-scale echo of the whole. The branches of a tree, the florets of a cauliflower, the bifurcations of a river—all are examples of natural fractals. The math eschews the smooth lines and planes of the Greek geometry we learn in school, but it has astonishingly broad applications wherever roughness is present—that is, nearly everywhere.

Some of his most important insights came, not from elaborate mathematical reasoning, but from a flash recognition of kinship between disparate images—the strange resemblance between diagrams concerning income distribution and cotton prices, between a graph of wind energy and of a financial chart. The creative essence of fractal geometry is to combine the formal and the visual. The ready intuition of fractal pictures has, today, made the subject a college course at Yale and other universities, and a popular addition to many high school math courses.

CHAPTER I Risk, Ruin, and Reward IN THE SUMMER OF 1998, the improbable happened. On Wall Street, the historic bull market of the New Gay ’90s was looking tired. There was no single, overwhelming problem—just a series of worries: recession in Japan, possible devaluation in China, and in Washington a president battling impeachment. Then came news that Russia, just two years earlier the world’s hottest emerging market, was hitting a cash crunch. Western banks and debt-traders would suffer; a few, it later emerged, were already near ruin.

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