| PMATH 370 |
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Project on Chaos or Fractals
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This material is from the Winter 2014 offering of PMATH 370, and is for reference only.
Other links
Topic
Your project should be in chaos or fractals and related to your areas
of interest.
The aim is to show that you understand a topic in chaos or fractals, and not
just write an essay extracted from other work.
This can best be done by explaining the topic in your own words, and then
doing some new examples.
Date Due
The project will be due by 3:45 p.m. on Friday April 4th
in my office MC 5086 or the Pure Math Office MC 5064/5065/5066.
If your project is all on the web, you can just e-mail me the URL
(and I will confirm by e-mail that I have received it and can read it).
Group work
The projects may be done individually, or in groups of up to four people.
A explainatory page indicating which person worked on which part of the
project should be submitted with the project.
The expectations of the project are the same regardless of whether you are
in a group, or working individually.
I highly encourage students to work in groups.
A discussion group on Learn has been set up to aid people in finding groups.
Details
You should first give a short abstract of your project.
Then you should most probably give a summary of the theory behind the project
and try to tie it in with what we covered in the course.
Finally you should give some examples, which will quite likely use computers.
You can submit pictures by just giving me their Web address.
In fact, your whole project could be on your Web pages.
You should make it clear what part of the project is your work, and what part is obtained from other sources, giving references to these sources.
If your project contains a program you wrote, you should give your
source code.
If your project includes a Java applet or program that runs on one particular
type of computer, you should include screen shots in case there are
problems running it.
Indicate if you would like your project to be made available to
future terms on the course website.
Length
Lengths of the project vary considerably depending on the type of project
being done.
I have included the some rough estimates below, based on the most
common projects.
- Essay without computer program/applets,
typically 7 - 8 pages, (1800-2100 words).
- Small essay + computer program,
4-5 page paper (1000-1400 words).
At most one page will be explaining the user
interface.
The paper must have meaningful mathematical content.
- Webpages will typically be somewhere between these two extremes,
depending on the number of applets (if any).
- Video, 10-15 minutes.
- If you wish to do a project in a non-standard format, discuss it with
me first so that we can figure out the expectations for the project.
Examples
- Interactive Web page on some aspect of chaos or fractals.
- Analyse the various algorithms for producing the Mandelbrot set or Julia sets.
- Write a program to generate a fractal landscape.
- Write a program to find the box-counting dimension of a set in the plane.
- Write a program to find the Lyapunov exponent of a function.
- Try to find iterated functions systems that will generate some standard sets.
- Use of chaos or fractals in an area you are interested in such as Music, Computer Graphics, Electronics, Physics, Chemistry, Biology, or Medicine.
- Analyse the Henon or other attractor.
- Analyse some generalization of Newton's method.
- Find the bifurcations for some parameterized family.
- Try to find conjugates, linear and non-linear, between various families of maps.
- Fractal image compression.
- Fractal knitting or crocheting.
- Find examples of maps that illustrate the Sharkovsky ordering.
- Construct plane-filling or space-filling curves.
- Give a mathematical proof of some theorem related to dynamical systems, chaos or fractals.
- You could delve deeper into some aspect of the course.
- Applications of fractals to some other area of study,
(ecology, medicine, meterology, geography, ....)