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# Fractal Geometry

## Module MA5207

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Module version of WS 2011/2

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2012WS 2011/2

### Basic Information

MA5207 is a semester module in German or English language at Master’s level which is offered irregular.

This module description is valid from WS 2010/1 to SS 2013.

90 h 30 h 3 CP

### Content, Learning Outcome and Preconditions

#### Content

Definition of fractal set; Iterated function systems (IFSs) and their properties; Construction of fractals via IFSs; Basic dimension theory; Approximation with fractals; Connection to dynamical systems; Fractal functions and fractal surfaces.

#### Learning Outcome

After a successful completion of the course, the student is able to construct fractal sets using iterated function systems, to analyze their properties and to derive connections to dynamical systems. In addition, the student is able to generate approximation models using fractal functions and fractal surfaces.

#### Preconditions

MA1002 Analysis 2, MA1102 Linear Algebra 2

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

VO 2 Fractal Geometry Massopust, P. documents

#### Learning and Teaching Methods

lecture, assignments

blackboard

#### Literature

B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, 1983 (einführend).
M. F. Barnsley, Fractals Everywhere, Morgan Kaufman, 2nd. Ed., 2000 (begleitend).
K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, Wiley, 2nd. Ed., 2003 (begleitend).
P. Massopust, Interpolation and Approximation with Splines and Fractals, Oxford University Press, 2010 (begleitend).
P. Massopust, Fractal Functions, Fractal Surfaces, and Wavelets, Academic Press, 1995 (weiterführend).

### Module Exam

#### Description of exams and course work

The module examination is based on a 30-minute oral exam. Students are able to construct fractal sets using iterated function systems, to analyze their properties and to derive connections to dynamical systems. In addition, students are able to generate approximation models using fractal functions and fractal surfaces.

#### Exam Repetition

The exam may be repeated at the end of the semester.

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