This course introduces the basic mathematical techniques of fractal geometry for diverse applications. It will explain how these techniques apply to digital imaging, image compression, special effects,  biological modelling, medical data representation and cryptography. The key ideas are introduced in an intuitive, hands-on manner.

Each student will be expected to select and complete a special project in one of the following areas: (i) 3D printing  of  fractal models ; (ii) fractal image magnification; (iii) fractal compression ; (iv) project chosen by the student with agreement from the lecturer.  There will be one computer lab meeting each week. 

Graduate students will attend all lectures/workshops including the Honours special lectures which will provide rigorous mathematical foundations and but they be assessed separately from undergraduate students.

On satisfying the requirements of this course, graduate students will have the knowledge and skills to: 

1. Explain the basic concepts of fractal geometry; (LO1) 

2. Be able to identify practical situations where fractal techniques may be applied; (LO2) 

3. Be able to build a fractal application in a practical area such as  digital imaging or biological modeling. (LO3) 

4. Be able to prove basic theorems and solve problems in the area of Iterated Function Systems. (LO4) 

 Assessment may be based on:

• Projects (25%; LO 1-4)

• Tutorials and Lab worksheets (25%; LO 1-4)

• 5 Assignments (25%l  LO 1-4)

• Mid-term Exam (25%; LO 1-4) 

36 lectures and approx. 10 workshops

Bachelor degree; with first year Mathematics.

First year Mathematics is required.

Fractals Everywhere, by Michael F. Barnsley, Third Edition (2012,  Dover).