Intro to Chaos and Fractals: Final Project Topics

Here are some ideas for final project topics. These are just suggestions; you are welcome to come up with other ideas or do some combination of these things.

• On several occasions, Ken Cline has asked me what the implications of "chaos theory" are for public policy and planning. Is everything unpredictable? As we learn more and more about complex interrelationships, is prediction or forcasting even possible? This project would be to try and answer that question for him. (We'd invite him to the presentation.)

• There have been many, many applications of chaos and fractals to different areas of biology. There are lots of models of ecosystems and populations dynamics that are chaotic. And lots of folks have used fractals and related ideas to describe and quantify a variety of physiological and other phenomena: the branching of trees, lungs, veins and arteries; the beats of normal and diseased hearts; nerve impulses; and the statistical properties of speech and music.

• Chaos and fractals have, arguably, have a significant impact on literature, art, and popular culture. A good project would be to trace some of these influences, perhaps reading some modern fiction or poetry and/or examining trends in modern art.

• There are some relatively simple programs that can be used to make amazing fractal images. A possible project could be to make some particularly cool images and explain the math behind them.

• John Guare's playe Six Degrees of Separation put forth the idea that all people are linked by no more than six acquaintances. Are populations really "connected" in this way? How are other sorts of networks connects? What about the relations among creatures in an ecosystem or the links and nodes of the internet? This is a topic of considerable current research; there was a nice article on it in the New York Times last week.

• Randomness, Causality, Explanation, Certainty, Uncertainty, Order, Disorder, Determinism, Reductionism, Wholism. What does "chaos theory" have to say about these ideas? Many philosophers have written about the implications of chaos. Your project would be to read and ponder, and then present.

• Cellular Automata.

Projects from Winter term 2001

• Chaos and Fractals in Art.
• Animated, evolving Julia sets.
• Chaos in music composition and analysis.
• Using fractals to make computer-generated landscapes.
• Building a chaotic water wheel and a Hele-Shaw cell.
• Fractals in nature.

Web page maintained by dave@hornacek.coa.edu.