Chaos and Fractals : Finding Hidden Order
A web page for Witt Sem 100
Fall 2005

"The scientist does not study nature because it is useful; he studies it because he delights in it and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living" - Henri Poincare (1854 - 1912)

"A mathematician who is not also something of a poet will never be a perfect mathematician"
 Karl Weierstrass (1815 - 1897)
"Now as Mandelbrot points out [...] .nature has played a joke on the mathematicians. The 19th century mathematicians may have been lacking in imagination, but nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all round us in nature." - Freeman Dyson, Characterizing irregularity, Science 200(1978) 677-678.

"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning  travel in a straight line ... Nature exhibits not simply a higher degree but an altogether different level of complexity". Benoit Mandelbrot

"The most exciting phrase to hear in science, the one that hearlds new discoveries is not 'Eureka' (I found it) but 'That's funny ..'" -Isaac Asimov
Course Description

"One of the great revolutions in science and mathematics in the last century was the realization that the universe is not always the predictable, clockwork place that it was thought to be. The new insights of fractal geometry and chaos theory that came out of this revolution have affected not only science and mathematics, but also fields as diverse as music, computer graphics, and economics. This course is an introduction to the ideas of fractals and chaos. Using these ideas, we will enter into a world in which simple rules give rise to almost unimaginable complexity and a fantastic and delicate beauty. Along the way we’ll investigate questions such as “Can a butterfly flapping its wings in Brazil really cause a tornado in Ohio?” and explore the infinite levels of detail of the most famous fractal, the Mandelbrot set. As a final project, you’ll be able to apply these concepts and techniques to an area of interest to you. You might choose to create a fractal musical composition, investigate why a perfectly regular heartbeat might not be as healthy as a somewhat irregular one, or study how chaos can be used in cryptography. This seminar meets the math reasoning requirement (M). "

Instructors

    Professor Elizabeth George - Department of Physics - egeorge@wittenberg.edu
    Professor Brian Shelburne  - Department of Mathematics and Computer Science - bshelburne@wittenberg.edu

Note : This site is always under-construction. As new and interesting sites are found over the summer, they will be added below

Mandelbrot Julia Explorer


Return to  Shelburne's Alternate HomePage