Prerequisites. First and second year of the Laurea Triennale
Teaching Methods. Traditional teaching with examples and exercises.
Verification of Learning. Oral colloquium and developement of SageMath routines.
More Information. If required, the course may be taught in English.
Objectives
Provide a modern and rigorous introduction to fractal objects. Collect together parts of mathematics dealt with in various courses of the laurea triennale, and use all of them to treat objects which are modern, interesting, and of impressive visualization. Learn how to use a powerful and free Computer Algebra System, such as SageMath.
Contents
Fractal objects. Iterated Function Systems. The box dimension. The Hausdorff measure and dimension. The chaos game and the use of free Computer Algebra Systems.
Texts
M. Barnsley and A. Vince, Developments in fractal geometry, Bull. Math. Sci. 3:299-348, 2013.
K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, 3rd edition, Wiley, 2014.
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