PMath 370 Chaos and Fractals

Fall 2006

University of Waterloo - Waterloo, Ontario, Canada

This course is designed to introduce a wide range of students to the mathematical foundations of chaos, fractals, and discrete dynamical systems. Many students are intrigued by the scientific, visual, and computing aspects of chaos and fractals, but do not have much idea of the mathematics involved. This mathematics can be introduced to a student who has a background of calculus and linear algebra.

Instructor

Instructor : Kevin Hare, Office MC 5086, Ext 35556.

Infinite Binary Fractal Trees

The information on Infinite Binary Fractal Trees was based on the PhD Thesis of Tara Taylor (mostly the first introductory chapter).
More information, with nice animiations.

Text

AUTHOR: Gulick, Denny.
TITLE: Encounters with chaos
CALL NUMBER: Q172.5.C45G85 1992 [on 1 day reserve]
IMPRINT: McGraw-Hill, c1992.
The book is out-of-print, but copies made by UW Courseware Solutions will be available from PIXEL PLANET MC 2018.

Course Outline

Periodic Points - iterates of functions, fixed points, basins of attraction, periodic points, attracting/repelling points, bifurcations, Sharkovsky order.
Chaos - Transitivity, strong chaos, conjugacy, linear functions, nonlinear maps.
Fractals - Dimensions, Julia sets, Mandelbrot sets, iterated function systems.
Anything else I happen to think is interesting at the time.

Course Mark

The mark in the course will be computed as follows.

Six Assignments [Due Sep 22, Oct 6, 20, Nov 3, 17, Dec 1] - 25% (or 15%)
Review of book, paper, web pages, or video [Due Oct 13] - 10%
Midterm test [on Fri Oct 27 in class] - 15%
Project or essay [Due on Monday Dec 4] - 20%
Final exam [December 9th, 9:00 am - 11:30 am, RCH 308] - 30% (or 40%)

Chaos and Fractal Resources

Books, articles, videos, web links, and programs on chaos and fractals.

Further Course Information

[Julia Set 1] [Lorenz Attractor] [Julia Set 2]

This page was last updated on by K. G. Hare