# Vorlesung: Fractal Geometry

## News

- I will not be on campus from July 1st until July 5th. The lecture for Wednesday, July 3rd, has been moved to
**Friday, July 19th**, at**10:30 AM**, in room**03.04.011**. - The oral examinations are scheduled to take place on
**August 22nd**and**August 23rd, 2013**. Students interested in taking the exam are requested to write their name on one of the sign-up sheets posted on my office door. (03.04.039)

## Organization

- Lectures (2 SWS)
- Lecturer: PD Dr. Peter Massopust
- Module Number: MA5207
- ECTS-Points: 5
- Time: Wednesdays, 12 - 2 PM
- Place: MI 02.08.011

## Contents

- Definition of Fractal Sets
- Iterated Functionen Systems and their Properties
- Construction of Fractal Sets via Iterated Function Systems
- Elementary Dimension Theory
- Approximation by Fractals
- Relation to Dynamical Systems
- Fractal Functions and Fractal Surfaces

## Problem Sets

- Übungsblatt 1
- Übungsblatt 2
- Übungsblatt 3
- Übungsblatt 4
- Übungsblatt 5
- Übungsblatt 6
- Übungsblatt 7
- Übungsblatt 8
- Übungsblatt 9
- Übungsblatt 10
- Übungsblatt 11
- Übungsblatt 12

## Literature

- B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, 1983 (basic)
- M. F. Barnsley, Fractals Everywhere, Dover Publications, New Edition 2012 (intermediate)
- K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, Wiley, 2nd. Ed., 2003 (intermediate)
- P. Massopust, Interpolation and Approximation with Splines and Fractals, Oxford University Press, 2010 (intermediate)
- P. Massopust, Fractal Functions, Fractal Surfaces, and Wavelets, Academic Press, 1995 (advanced)