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Each of the kiosks below will lead you into a different facet of the exciting world of patterns in Nature. Many of these patterns are fractals. Fractal forms are ubiquitous in Nature, and especially likely to arise when randomness plays a large role during the pattern’s development. The experiments and examples in this exhibit demonstrate some of the many ways that branching patterns arise in Nature from the conflict between random and constraining forces:
Introduction: Exploring Fractals
Fractal geometry and chaos theory are providing us with a new perspective to view the world. For centuries we’ve used the line as a basic building block to understand the objects around us. Chaos science uses a different geometry called fractal geometry. Fractal geometry is a new language used to describe, model and analyze complex forms found in nature.
A few things that fractals can model are:
human body rhythms
animal group behavior
and more …
This is how nature creates a magnificent tree from a seed the size of a pea … or broccoflower
Fractal dimension can measure the texture and complexity of everything from coastlines to mountains to storm clouds. We can now use fractals to store photographic quality images in a tiny fraction of the space ordinarily needed.
Fractals win prizes at graphics shows and appear on tee – shirts and calanders. Their chaotic patterns appear in many branches of science. Physicists find them on their plotters. Strange attractors with Fractal turbulence appear in celestial mechanics. Biologists diagnose dynamical diseases. Even pure mathematicians such as Bob Devaney, Heinz-Otto Peitgen and Richard Voss go on tour with slide shows and videos of their research.
Fractals provide a different way of observing and modeling complex phenomena than Euclidean Geometry or the Calculus developed by Leibnitz and Newton. An arising cross disciplinary science of complexity coupled with the power of desktop computers brings new tools and techniques for studying real world systems.
(c) Copyrighted 1994,1995,1996,and 1997 by Mary Ann Connors. All rights reserved. If you wish to use any of the text or images in Exploring Fractals please contact its author Mary Ann Connors at the following address. Thank you.
Dr. Mary Ann Connors
Department of Mathematics & Statistics
Lederle Graduate Research Tower
University of Massachusetts
Amherst, MA 01003
…This is a collection of pages meant to support a first course in fractal geometry for students without especially strong mathematical preparation, or any particular interest in science. Each of the five pages contains examples of fractals in the arts, humanities, or social sciences. It is our hope, supported by over a decade of experience teaching such courses, that students will find this material both accessible and interesting. They will see fractal geometry gives a new way of looking at their world; that they have been surrounded by natural patterns, unsuspected but easily recognized after only an hour’s training; and that often they can find new instances of these patterns on their own…