Fractals, Chaos and Dynamical Systems Team

Team Mentor: Dr. Dipendra Sengupta

Team Members

Donald Charity, Freshman/Math Major
Cory Ellis, Junior/Applied Math Major
Brian Jordan, Senior/Applied Math Major
Donald Charity, Freshman/Math Major
Tammara Ward, Junior/Math Major
Lakisha Mundon, Sophomore/Math Major
Ayonda Moore, Junior/Math Major


Most naturally occuring processes are inherently nonlinear and can give rise to very complex behaviors. Even very simple mathematical models can exhibit behavior that give rise to extremely convoluted (and often very beautiful) fractal shapes. The discovery of this fundamentally new area of mathematics has been crucially dependent on computational intensive graphic methods and has given birth to a radically new paradigm for mathematical research: experimental research.

In this project we will perform experimental mathematical investigation. The mathematical contents will comprise fractals, nonlinear dynamics and mathematical chaos.

We will study the orbits of a family of quadratic dynamical systems and investigate the period doubling route to chaos. We will design and develop mathematical materials and Mathematica programs necessary to do the investigation.

We will apply fundamental mathematical concepts to a wide variety of physical, biological and social processes (e.g., population growth, measles problem, growth of plant, problems of epidemiology, and the economics of arms race). The deep connection between geometry and nonlinear dynmaics will be explored and computer programs will be developed to generate fractal maps and pictures of compelling beauty. Finally, through guided work in experimental mathematics students will acquire a deeper understanding of mathematical and scientific thinking.

Brian Jordan, Ayonda Moore, and Donald Charity prepare for the SOARS '96 Conference.

Dr. Sengupta assists Brian Jordan with a problem.