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 modeling, medical data representation and cryptography. The key ideas are introduced in an intuitive, hands-on manner, although all students are invited to sit in on the HPO option special lectures which will provide rigorous mathematical foundations. 

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. 

Honours pathway option (HPO)

Students doing the HPO option will participate in an additional lecture each week. These may be related to the material in the basic course, but will be focused on exhibiting and understanding the general theory of Iterated Function Systems. 

On satisfying the requirements of this course, 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. (HPO only)  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 1-3)
• Tutorials and Lab worksheets (25%; LO 1-3)
• 5 Assignments (25%l  LO 1-3)
• Mid-term Exam (25%; LO 1-3)

24 lectures and approx. 10 workshops. Plus 12 additional lectures for HPO

Honours studenst need to complete MATH2305 or MATH2405

Prerequisite:  MATH1013 or equivalent.

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