Visualizing Chaos in Classic Dynamical Systems
The advent of the personal computer and enhancements to computer graphics has greatly affected the way scientific research is conducted. The study of dynamical systems has experienced a rebirth as a result of these improvements. As a mainly geometric and topological study, any further improvements to the way systems are visualized should improve the understanding of the underlying dynamics. In this study several classic examples of chaotic dynamical systems were emulated using the Mathematica software package. In particular several simple two-dimensional systems, the Lorenz attractor, and the Mandelbrot and Julia sets were addressed. Once they were satisfactorily recreated a number of improvements such as animation and coloration were employed in order to enhance the understanding of the underlying attributes of the particular system in question.
School:
San Jose State University
Department:
Mathematics and Computer Science
Research Advisor:
Dr. Klaus Witz
Department of Research Advisor:
Curriculum and Instruction
Year of Publication:
2004