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master's thesis
Hausdorffova dimenzija i fraktalni skupovi
2023. urn:nbn:hr:126:239386
Vugrinec, Leo
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

Cite this document

Vugrinec, L. (2023). Hausdorffova dimenzija i fraktalni skupovi (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:239386

Vugrinec, Leo. "Hausdorffova dimenzija i fraktalni skupovi." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:239386

Vugrinec, Leo. "Hausdorffova dimenzija i fraktalni skupovi." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:239386

Vugrinec, L. (2023). 'Hausdorffova dimenzija i fraktalni skupovi', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 15 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:239386

Vugrinec L. Hausdorffova dimenzija i fraktalni skupovi [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2023 [cited 2025 January 15] Available at: https://urn.nsk.hr/urn:nbn:hr:126:239386

L. Vugrinec, "Hausdorffova dimenzija i fraktalni skupovi", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:126:239386

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Metadata
TitleHausdorffova dimenzija i fraktalni skupovi
Title (english)Hausdorff Dimension And Fractal Sets
AuthorLeo Vugrinec
MentorDanijel Grahovac (mentor)
Committee memberNenad Šuvak (predsjednik povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
Committee memberIvan Papić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2023-12-15, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
Početak diplomskog rada uključuje uvođenje i osnovno objašnjenje temeljnog pojma fraktala. U radu se navode i definiraju pojmovi kao što su mjera, topološki prostor i pokrivač te se uz pomoć njih detaljno objašnjava pojam Hausdorffove mjere. Uz to, navode se i neka njena ključna svojstva te sličnosti s ostalim vrstama mjera. Kasnije se definira Hausdorffova dimenzija te se pobliže promatraju njena svojstva koja su esencijalna za daljnje analiziranje fraktala. Nakon toga se provode konstrukcije mnogih poznatih fraktala te se računaju njihove Hausdorffove dimenzije.
Abstract (english)
The start of this paper includes introduction and general description of a term fractal. Terms like measure, topological space and cover are defined and used to explain what Hausdorff measure is. Some of its properties and connections to other measures are also stated in this paper. Later, Hausdorff measure is defined and its properties that are essential for the analysis of fractals are described. After that, many fractals are constructed and their Hausdorff dimensions are calculated.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:239386
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2025-01-15 11:34:14