2018•K-State Research Exchange (Kansas State University)Open access
Introduction to fractal dimension
Ghder Aburamyah
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Abstract
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.With great appreciation, I would like to thank my major advisor Dr. Hrant Hakobyan for his help and guidance during the preparation of this report.I also would like to express my gratitude to the members of my examination committee, Dr. Sarah Reznikoff
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