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Fractal sets and dimensions
Linköping University, Department of Mathematics.
2006 (English)Independent thesis Basic level (professional degree), 20 points / 30 hpStudent thesis
Abstract [en]

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.
Keyword [en]
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
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-7320ISRN: LiTH-MAT-EX--06/06--SEOAI: oai:DiVA.org:liu-7320DiVA: diva2:22333
Presentation
2006-05-02, Asylen, A-huset, Linköpings universitet 581 83 LINKÖPING, LINKÖPING, 13:15
Uppsok
fysik/kemi/matematik
Supervisors
Examiners
Available from: 2006-12-05 Created: 2006-12-05

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf