Fractal Geometry
Module MA5207
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 SS 2012 (current)
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 2012 | WS 2011/2 |
Basic Information
MA5207 is a semester module in English language at Master’s level which is offered irregular.
This module description is valid from WS 2010/1 to SS 2013.
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 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
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VO | 2 | Fractal Geometry | Massopust, P. |
documents |
Learning and Teaching Methods
lecture, assignments
Media
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).
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.