Fractal sets and dimensions
Independent thesis Basic level (professional degree), 20 points / 30 hpStudent thesis
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.
Place, publisher, year, edition, pages
Matematiska institutionen , 2006. , 65 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
IdentifiersURN: urn:nbn:se:liu:diva-7320ISRN: LiTH-MAT-EX--06/06--SEOAI: oai:DiVA.org:liu-7320DiVA: diva2:22333
2006-05-02, Asylen, A-huset, Linköpings universitet 581 83 LINKÖPING, LINKÖPING, 13:15