<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>
| Identifer | oai:union.ndltd.org:UPSALLA/oai:DiVA.org:liu-7320 |
| Date | January 2006 |
| Creators | Leifsson, Patrik |
| Publisher | Linköping University, Department of Mathematics, Matematiska institutionen |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, text |
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