After successful completion of the course, students are able to...

Remember - students will be able to recall basic properties of fractals and the principles of fractal geometry.

Understand - students will be able to understand principles and methods of fractal geometry, such as self-similarity, fractal dimension, dynamic systems, approximations of fractals and visualization techniques.

Apply - students will be able to apply methods of fractal geometry, either using existing or self-implemented applications.

Analyse - students will be able to analyse shapes using methods from fractal geometry and predict the chaotic behaviour of dynamic systems.

Evaluate - students will be able to assess which shapes are suitable to be analysed and generated using fractal geometry.

Create - students will be able to implement methods from fractal geometry in applications and use them to generate fractals. They will also be able to use these techniques for the procedural modelling of natural phenomena.

• Introduction and comparison of fractal and classic geometry
• Basics of fractal geometry (metric spaces, dynamic systems, fractal dimension)
• Iterated Function Systems (IFS)
• Julia-Sets and Mandelbrot-Set
• Stochastic Fractals
• L-Systems
• Chaos Theory
• Video presentation

Introduction to the concepts of fractal geometry.

Explanation of the different classes of fractals and their properties.

Illustration of fractal geometry through images and videos.

Discussion of algorithms for the visualization of fractals. 

Demonstration of fractal applications.

ECTS breakdown (estimation, recommendation):

30 hrs. lecture

45 hrs. preparation and examination

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75 hrs. equals to 3 ECTS each of 25 hrs.

There are the following 3 examination modalities:

1. Three short written tests during the lecture. These will take place at the beginning of each lecture unit and will last 15min. Those who miss one of these dates can make up for it by taking a short oral exam by appointment. Those who do not choose this examination mode can come to the lectures 15min. later on the examination days. Dates: 22.11., 20.12. and 24.01.24.

2. An oral examination on the entire lecture material will be taken. Dates are available by appointment at the beginning and end of each semester.

3. A presentation will be given in one of the last two lectures. The lecture must deal with a specific topic of fractal geometry and must complement or deepen one of the main topics of the lecture.

Basic mathematical knowledge