Images of Chaotic Dyanamical Systems:

Julia sets, Lorenz attractor, Cauliflower, Pipe Organs

On this page we present various topics from chaotic dynamical systems:
Here we present a quick review of what a Julia set is. In particular, orbits of points are discussed and how the computer uses them to color both the "inside" and "outside" of the Julia set.
If a Julia set has an attracting cycle, it's pretty easy to find the points on the cycle. But here's a way to locate the repelling cycles of the Julia set, of any given period.
My thesis student Chris Danforth wanted to study the Lorenz attractor. Here are a couple pictures and animations of this amazing object.
The cauliflower is a perfect example of a 3?-D fractal found in nature.
Can the display pipes of a pipe-organ be considered a fractal? Consider this!

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© 2001 by Chip Ross
Associate Professor of Mathematics
Bates College
Lewiston, ME 04240