- Can take many forms -- need not be a paper. We will discuss as
a class whether or not we want to have a set of presentations open to
the coa community, or if we just want to present to the class.
- Should be on some topic that's interesting to you.
- You and I share responsibility for the project. I will try to
meet with you all individually and discuss possible projects. But you
also need to take some initiative; if you're feeling lost or confused,
be assertive and find me sooner rather than later.
- I strongly encourage you to work on projects in groups. Perhaps
you'll end up doing separate projects, but maybe a few of you have
broadly similar interests. If this is the case, I suggest doing some
common background readings and meeting to discuss as a group.
Preliminary Project Guidelines
Here are some properties of an excellent final project:
- Most importantly, you should learn something in the course of
doing your project. Ideally, you'll find one or two ideas that you'll
want to explore thoroughly.
- You should meet all deadlines.
- Whatever medium you choose -- talk, paper, etc -- your project
should be well presented. You should have a clear audience in mind.
- Your project should be more than a "book" report. You should do
something. This might entail building something, writing or
experimenting with computer programs, or doing a bunch of problems.
- Your project should be something you work on over several weeks.
It should not be hastily completed during week 9.
- In most cases, you should consult several references, not just
one. It is also desirable (although in many cases this won't be
feasible) for you to consult a primary reference or two in addition to
Possible Project Ideas
- Further exploration of the logistic map.
- Detailed proof/demonstration of chaos,
- Examination of universality
- Sarkovski's theorem on the ordering of periodic orbits.
- Measures of randomness and complexity. How can we quantify how
random or unpredictable a system is? How can we quantify how
"complex" or "structured" or "complicated" or "intricate" a system is?
- Cellular Automata
- Develop lesson plans for a high school or elementary class. Or,
develop materials for the introductory chaos and fractals course to be
taught in the winter.
- Detailed exploration of the Mandelbrot and Julia sets. This could
involve doing some graphical experiments and/or proving some stuff.
- Applications of fractals in the geosciences. Looking at the type
of networks formed by river basins might be especially timely, given
that there's a "monster" course in rivers coming up.
- Evolution and Adaptation
- Dynamical models of of evolution.
- Genetic algorithms.
- Evolving cellular automata. (Our book has a section on this.)
- Population Dynamics. Effects of finite size populations.
- Models of Ecosystems
- Agent-based models
- Focus on a particular application. Dynamics arises in tons of
scientific (and unscientific) situations.
- Do an experiment. Collect some data. Or, work with some data
sets that are publicly available. Build and analyze a chaotic system.
- Scaling in biological systems. Why does metabolism rate depend on
the mass of a creature in the way that it does?
- Differential Equations. There are tons of systems that are
modeled via differential equations.
- Population dynamics
- Mechanical systems (pendulums and springs and stuff)
- Chemical reactions
- Agent-based simulations
- Game theory
[ Dave ]
[ COA ]
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