Fractal Summer 2009 begins...

I've been going through the book "Fractals, Graphics and Mathematics Education" by Mandelbrot and Frame. There are many interesting and accessible articles in it, and some useful links are also provided. Unfortunately most of them are no longer available.



The only link that I could still find up is Robert Devaney's:

http://math.bu.edu/DYSYS/dysys.html

Actually Robert Devaney has many interesting links that you can get to from his homepage:

http://math.bu.edu/people/bob/



A wish-list of activities/topics for the summer students:

• MathSciNet- get them to use this to search for research papers


• Google Scholar- another good source for finding research papers


• Mathematica- a software program that is useful for writing programs for fractals. I already have a program for binary trees.


• Explore binary fractal trees: symmetric, asymmetric, general- this can be done using mathematica, but also by going through papers (Mandelbrot and Frame, Brown, etc)


• LaTex- learn to write basic articles


• Sierpinski relatives- explore, make observations


• Learn basic background about fractals: contractive mappings, IFS, fractal dimension, self-similarity


• Learn basic background about topology: notions like connectedness, simply vs multiply connected, how topology can distinguish between 2 fractals that have the same dimension


• Learn about the golden ratio and connections between fractals and the golden ratio- my paper for the MAA book is a good start


• Learn about applications of fractals- what is interesting?


• Look at interesting examples/classes of fractals


• Antoine's necklace


• Indra's Peals


• Chaos Game

Some goals:

• Encourage students to pursue what interests them, to find their own questions


• Prepare for some kind of presentation- either at APICS or StFX student research day (or both)