Fractals

Course code MATH3710Units 10Level 3000Faculty of Science and Information TechnologySchool of Mathematical and Physical Sciences

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.

Not available in 2015

ObjectivesBy 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.
ContentThe 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
Transitionn/a
Industrial Experience0
Assumed KnowledgeMATH1220 Advanced Mathematics 1220
or
MATH2340 Algebra and Geometry
Modes of DeliveryInternal Mode
Teaching MethodsLecture
Assessment Items
Essays / Written Assignments
Examination: Formal
Other: (please specify)Homework
Contact HoursLecture: for 3 hour(s) per Week for Full Term