Not available in 2014

Previously offered in 2007, 2006, 2005

Fractal geometry emerged as a discipline in its own right only in the latter part of the 20th century when the power of the computer enabled ready visualization of the objects under study. Even so, interest in the subject has been strong across a broad spectrum of the mathematical and scientific community and it has grown into a large and diverse body of knowledge.

Assuming that this is the first time that you have formally studied fractals this course aims to provide an introduction to fractal geometry and its applications.

Objectives By the completion of the course the student should be able to:

1. Use computer software to generate many types of fractals.
2. Explain, and work with, the various notions of dimensions as used in fractal geometry.
3. Explain the notion of lacunanty and its relationship to fractal dimension and to be able to work with this concept.
4. Represent fractals using Iterated Function Systems and understand the mathematics associated with them.
5. Appreciate the role of randomness in the construction of fractals used to model nature by construction examples of such fractals and studying their properties.
Content The course covers the following the topics and their applications:

* Introduction to Fractals
* Dimension
* Lacunarity
* Iterated Function Systems
* Attractors of Dynamical Systems
* Fractals from random processes
* Cellular Automata
Replacing Course(s) n/a
Transition n/a
Industrial Experience 0
Assumed Knowledge MATH1220 Advanced Mathematics 1220
or
MATH2340 Algebra and Geometry
Modes of Delivery Internal Mode
Teaching Methods Lecture
Assessment Items
Essays / Written Assignments
Examination: Formal
Other: (please specify) Homework
Contact Hours Lecture: for 3 hour(s) per Week for Full Term