Global ETD Search

1	Introduction to fractal dimension Aburamyah, Ghder January 1900 (has links) Master of Science / Department of Mathematics / Hrant Hakobyan / When studying geometrical objects less regular than ordinary ones, fractal analysis becomes a valuable tool. Over the last 40 years, this small branch of mathematics has developed extensively. Fractals can be defined as those sets which have non-integer Hausdorff or Minkowski dimension. In this report, we introduce certain definitions of fractal dimensions, which can be used to measure a set’s fractal degree. We introduce Minkowski dimension and Hausdorff dimension and explore some examples where they coincide, as well as other examples where they do not. FractalDimension Fractaldimension Fractal Dimension Hausdorff dimension Minkowski dimension
2	Fractal sets and dimensions Leifsson, Patrik January 2006 (has links) <p>Fractal analysis is an important tool when we need to study geometrical objects less regular than ordinary ones, e.g. a set with a non-integer dimension value. It has developed intensively over the last 30 years which gives a hint to its young age as a branch within mathematics.</p><p>In this thesis we take a look at some basic measure theory needed to introduce certain definitions of fractal dimensions, which can be used to measure a set's fractal degree. Comparisons of these definitions are done and we investigate when they coincide. With these tools different fractals are studied and compared.</p><p>A key idea in this thesis has been to sum up different names and definitions referring to similar concepts.</p> box dimension Cantor dust Cantor set dimension fractal Hausdorff dimension measure Minkowski dimension packing dimension Sierpinski gasket similarity space-filling curve topological dimension von Koch curve Applied mathematics Tillämpad matematik
3	Fractal sets and dimensions Leifsson, Patrik January 2006 (has links) Fractal analysis is an important tool when we need to study geometrical objects less regular than ordinary ones, e.g. a set with a non-integer dimension value. It has developed intensively over the last 30 years which gives a hint to its young age as a branch within mathematics. In this thesis we take a look at some basic measure theory needed to introduce certain definitions of fractal dimensions, which can be used to measure a set's fractal degree. Comparisons of these definitions are done and we investigate when they coincide. With these tools different fractals are studied and compared. A key idea in this thesis has been to sum up different names and definitions referring to similar concepts. box dimension Cantor dust Cantor set dimension fractal Hausdorff dimension measure Minkowski dimension packing dimension Sierpinski gasket similarity space-filling curve topological dimension von Koch curve Applied mathematics Tillämpad matematik
4	Sur la dimension de Minkowski des quasicercles / On Minkowski dimension of quasicircles Le, Thanh Hoang Nhat 05 October 2012 (has links) Pour accéder au résumé en français à la fin de la thèse, ouvrir le fichier du texte intégral / Pour accéder au résumé en anglais à la fin de la thèse, ouvrir le fichier du texte intégral Dimension de Minkowski Dimension de Hausdorff Fonction de Bloch Question ouverte de Mc Mullen Martingale dyadique Mesure de Kahane Série lacunaire Quasicercles Minkowski dimension Hausdorff dimension Bloch function Mc Mullen’s open question Dyadic martingale Kahane measure Lacunary series Quasicircles

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