Mathematics 439: The Mathematics of Fractals and Chaos
Fractals are intricate shapes like the one above, often exhibiting "self-similarity," so that if
one zooms in on a region, the magnified region still may have just as complicated and rich
an appearance as before. The name "fractal" indicates that the "dimension" of the shape
could be a fraction, not necessarily a whole number. Fractals can be used to model
complicated situations where objects like circles and parallelograms are inadequate.
Fractals also yield very interesting computer pictures. Such concepts will be explored in
Fall 2013, 3 credits
Stephen J. Willson
Office: Carver 411
MWF 2:10-3:00 pm in Sweeney 1160.
The first class is Monday, August 26, 2013.
There are no classes on Labor Day (September 2) and Thanksgiving Break (the week
of November 25- 29).
Tentatively these will be MTWThF 1:10-2:00 in 411 Carver. Please also feel free to make an appointment if the office hours are inconvenient for you.
The final exam is scheduled in the regular classroom, Sweeney 1160, on Wednesday, December 18, 2:15-4:15 pm.
Current homework assignments:
To obtain recent assignments and current information about course requirements, click here.
Selected lecture notes:
Current course grades
Current course grades and all recorded scores are available on Blackboard.
Iterated function systems; periodic points; algorithms for generation of fractals; fractal dimension; Julia sets and the Mandelbrot set; chaos. Nonmajor graduate credit.
Chaos: An Introduction to Dynamical Systems, by Kathleen T. Alligood, Tim D. Sauer, and James A. Yorke (Springer).
Tentative syllabus (subject to change):
- Iteration of one-dimensional maps
- Julia sets and the Mandelbrot set
- Fractals and fractal dimension
- Two-dimensional maps
Grades will be based on points accumulated. There will be graded problem sets
approximately each week. There will be one hour exam. Students will either take a final exam or turn in an individual project. Course grades may include a plus or a minus.
Computer and calculator usage:
Students will use computers or calculators to draw or analyze some fractals and dynamical systems by a variety of methods.
Computer links about fractals:
There are a huge number of web sites associated with fractals, and a search on Google for fractals will have a huge number of hits. Here are a few URLs to get started:
Applets and other tools illustrating fractals and chaos:
Please address any special needs or special accommodations with me at the beginning of the semester or as soon as you become aware of your needs. Those seeking accommodations based on disabilities should obtain a Student Academic Accommodation Request (SAAR) form from the Disability Resources (DR) office (515-294-6624). DR is located on the main floor of the Student Services Building, Room 1076.
Information about the instructor: For more information about the
Last updated August 23, 2013.