Fractals In Science

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Fractals in Science

Applying fractal geometry to science is bringing about a breakthrough in our understanding of complex systems in nature that show self-similar or self-affine features. Self-similar and self-affine processes appear everywhere in nature, in galaxies and landscapes, in earthquakes and geological cracks, in aggregates and colloids, in rough surfaces and interfaces, in glassy materials and polymers, in proteins as well as in other large molecules. Fractal structures appear also in the human body; well known examples include the lung and the vascular system. Furthermore, fractal geometry is an important tool in the analysis of phenomena as diverse as rhythms in music melodies and in the human heart beat and DNA sequences. Since the pioneering work of B.B. Mandelbrot, this interdisciplinary field has expanded very rapidly. The scientific community applying fractal concepts is very broad and ranges from astronomers, geoscientists, physicists, chemists and engineers to biologists and those engaging in medical research.
The Fractal Self

Author: John L. Culliney
language: en
Publisher: University of Hawaii Press
Release Date: 2017-07-31
Our universe, science reveals, began in utter simplicity, then evolved into burgeoning complexity. Starting with subatomic particles, dissimilar entities formed associations—binding, bonding, growing, branching, catalyzing, cooperating—as “self” joined “other” following universal laws with names such as gravity, chemical attraction, and natural selection. Ultimately life arose in a world of dynamic organic chemistry, and complexity exploded with wondrous new potential. Fast forward to human evolution, and a tension that had existed for billions of years now played out in an unprecedented arena of conscious calculation and cultural diversity. Cooperation interleaving with competition; intimacy oscillating with integrity—we dwell in a world where yin meets yang in human affairs on many levels. In The Fractal Self, John Culliney and David Jones uncover surprising intersections between science and philosophy. Connecting evidence from evolutionary science with early insights of Daoist and Buddhist thinkers, among others, they maintain that sagely behavior, envisioned in these ancient traditions, represents a pinnacle of human achievement emerging out of our evolutionary heritage. They identify an archetype, “the fractal self,” a person in any walk of life who cultivates a cooperative spirit. A fractal self is a sage in training, who joins others in common cause, leads from within, and achieves personal satisfaction in coordinating smooth performance of the group, team, or institution in which he or she is embedded. Fractal selves commonly operate with dedication and compassionate practice in the service of human society or in conserving our planet. But the competitive side of human nature is susceptible to greed and aggression. Self-aggrandizement, dictatorial power, and ego-driven enforcement of will are the goals of those following a self-serving path—individuals the authors identify as antisages. Terrorist leaders are an especially murderous breed, but aggrandizers can be found throughout business, religion, educational institutions, and governments. Humanity has reached an existential tipping point: will the horizon already in view expand with cooperative progress toward godlike emergent opportunities or contract in the thrall of corrupt oligarchs and tribal animosities? We have brought ourselves to a chaotic edge between immense promise and existential danger and are even now making our greatest choice.
Fractals and Multifractals in Ecology and Aquatic Science

Ecologists sometimes have a less-than-rigorous background in quantitative methods, yet research within this broad field is becoming increasingly mathematical. Written in a step-by-step fashion, Fractals and Multifractals in Ecology and Aquatic Science provides scientists with a basic understanding of fractals and multifractals and the techniques fo