Fractals and Chaotic Dynamical Systems

Course: MA325-01, and CSSE 325-01, Spring 2007 - 4 credits
Instructor: Allen Broughton
Time & Place: Period 3 MTRF G220
Prerequisite: MA 222 and CSSE 220

Per the course description we will

• Emphasize the mathematical and computer graphics foundations behind fractal images and the relationship between chaotic dynamics and fractal geometry.

We will look at the following topics

• Self-similar fractals,
• random fractals with Brownian motion,
• Fractals generated from dynamical systems.
• Fractal dimensions.
• Iterated Function Systems.
• Chaos in one-dimensional maps.
• Controlling chaos.
• Mandelbrot and Julia sets.

Computer graphics topics will be covered as needed to as needed to create interesting images arising from fractal geometry and chaotic dynamics.

Below are three interesting pictures created from iterated function systems and and chaotic dynamical systems The images are from Wikipedia.

Fern image created from an Iterated function system	Detailed portion of the Mandelbrot set showing mini Mandelbrot sets	A Julia set