Intro to Chaos and Fractals: Final Project
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.
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