"A fractal is an object or quantity that displays self-similarity , in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension . The prototypical example for a fractal is the length of a coastline measured with different length rulers . The shorter the ruler , the longer the length measured, a paradox known as the coastline paradox . "
Eric W. Weisstein. "Fractal." From MathWorld --A Wolfram Web Resource. http://mathworld.wolfram.com/Fractal.html
" Many people are immediately drawn to the bizarrely beautiful images known as fractals . Extending beyond the typical perception of mathematics as a body of sterile formulas, fractal geometry mixes art with mathematics to demonstrate that equations are more than just a collection of numbers. With fractal geometry we can visually model much of what we witness in nature, the most recognized being coastlines and mountains. Fractals are used to model soil erosion and to analyze seismic patterns as well. But beyond potential applications for describing complex natural patterns, with their visual beauty fractals can help alter students' beliefs that mathematics is dry and inaccessible and may help to motivate mathematical discovery in the classroom.
A popular representation of fractal geometry lies within the Mandelbrot set, named after its creator Benoit B. Mandelbrot who coined the name "fractal" in 1975 from the Latin fractus or "to break" (Jürgens et al., 1990). The Mandelbrot set ( figure 1 ) is the set of all points that remain bounded for every iteration of z = z*z + c on the complex plane, where the initial value of z is 0 and c is a constant (Jürgens et al., 1992)"
National Center for Supercomputing Applications, Education Group
rpanoff@ncsa.uiuc.edu and jgasaway@ncsa.uiuc.edu
WHAT IS A FRACTAL?
"A fractal is an object that displays self-similarity at various scales. In other words, if we zoom in any portion of a fractal object, we will notice the smaller section is actually a scaled-down version of the big one. "
THE NATURE OF FRACTALS, 1:6
This article explains some basic principles of fractal geometry, from its "discovery" to its application in science and art. Click here to download an Acrobat Reader version of this article for off-line reading.
Juan Luis Martínez
T h i r d . A p e x . t o . F r a c t o v i a
"The Dance of Chance exhibit is a collaboration between the Center for Polymer Studies and the Boston Museum of Science . The exhibit is based on current research pursued by CPS scientists and collaborating scientists around the world. The focus of the exhibit is the emergence of patterns in Nature from physical and biological processes which on the microscopic level appear to be dominated by chance. "
This material is based upon work supported by the National Science Foundation under Grant No. ESI-9353490. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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