"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Fractal Geometry
Code
Semes-
ter
Hours: C+S+L
Type
Section
MO055
6
2+0+1
optional
Informatica
MO055
6
2+0+1
optional
Matematică-Informatică
Teaching Staff in Charge
Assoc.Prof. SOOS Anna, Ph.D.,  asoosmath.ubbcluj.ro
Aims
Introduction in fractal theory: selfsimilarity, Hausdorff measure and dimension, invarinat sets and measures. Applications of fractals.
Content
1. Contraction principle. Iterated function system
2. Hausdorff measure
3. Hausdorff dimension
4. Invariant sets, fractals
5. Invariant measures, fractal measures.
6. Fractal functions.
7. Selfsimilarity
8. Similarity dimension
9. Stocastic fractals
10. Aplications: Brownian motion. Fractal compression. Virtual reality using fractals.
References
1. G.A.Edgar: Measure, Topology, and Fractal Geometry, Springer, 1990.
2. K.J.Falconer: Techniques in fractal geometry, John Wiley & Sons, 1997.
3. B.Mandelbrot: The Fractal Geometrie of Nature,W. H. Freeman and Company, New York, 1977.
4. A. Soos: Contraction methods in fractal theory, Cluj University Press, 2003
Assessment
Exam
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject