Fractal Geometry |
ter |
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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 |