Modul

The module will be completed with an oral exam (20 - 30 min).

Students

• can name and explain important terms and concepts of fractal geometry;
• know important results of dimension theory and can apply them to examples;
• have the ability to use specific methods for the analysis of fractal structures;
• are able to construct fractals and random fractals with certain prescribed properties;
• master important proof techniques in fractal geometry and are able to at least sketch the more difficult proofs;
• are able to work self-organized and in a reflective manner;
• are prepared, to write a thesis in the field of fractal geometry.

None

• iterated function systems and self-similar sets
• chaos game algorithm
• random fractals
• fractal dimension theory
• Hausdorff measure and dimension
• packing measure and dimension
• Minkowski contents
• methods of computing dimension
• self-similar measures and multifractals
• dimension of measures

The contents of the courses Analysis 3 (measure theory) and Probability theory are recommended.

Total workload: 180 hours

Attendance: 60 h

•  lectures, problem classes and examination

Self studies: 120 h

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research on the course content,
• preparation for the module examination