Subject: Fractal Geometry	Code: MO055	

Semester	 Hours: C+S+L	Type	 Section	
6	2+0+1	optional	Computer Science	
6	2+0+1	optional	Mathematics-Computer Science	

Teaching Staff in Charge	Assoc.Prof. SOOS Anna, Ph.D., asoos@math.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	
Selective 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, 200	
Assessment	Exa