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master's thesis
Klasični fraktali
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:397648
Filić, Andrea
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Filić, A. (2019). Klasični fraktali (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:397648

Filić, Andrea. "Klasični fraktali." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:397648

Filić, Andrea. "Klasični fraktali." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:397648

Filić, A. (2019). 'Klasični fraktali', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:397648

Filić A. Klasični fraktali [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:397648

A. Filić, "Klasični fraktali", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:397648

Metadata
TitleKlasični fraktali
AuthorAndrea Filić
MentorMatija Kazalicki (mentor)
Committee memberMatija Kazalicki (predsjednik povjerenstva)
Committee memberSiniša Slijepčević (član povjerenstva)
Committee memberSnježana Lubura Strunjak (član povjerenstva)
Committee memberGoranka Nogo (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-11-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Točke, pravci, geometrijski likovi i tijela su savršeni oblici i njima je prirodu ponekad nemoguće opisati. Dosta oblika u prirodi je nepravilno, neravno, rekli bismo, kaotično, stoga se u takvim slučajevima koristi fraktalna geometrija. Ova grana matematike razvila se tek krajem dvadesetog stoljeća i našla primjenu u znanosti, tehnologiji, medicini pa čak u astronomiji. U ovom radu je obrađen pojam fraktala te nekoliko klasičnih fraktala - Cantorov skup, trokut i tepih Sierpińskog, Kochova krivulja i pahuljica, Pitagorino stablo, Juliaov skup i Mandelbrotov skup. Svakom od njih opisano je njihovo svojstvo samosličnosti te izračunata dimenzija samosličnosti koja se razlikuje od pojma dimenzije kakvu poznajemo u euklidskoj matematici.
Abstract (english)
Points, lines, polygons and solids are perfect shapes and the nature sometimes cannot be described by them. Many shapes in nature are irregular, rugged, or we could say, chaotic, so in these cases we use fractal geometry. This part od mathematics began to develop at the end of twentieth century and found its application in science, technology, medicine, even in astronomy. This paper presents fractals and describes some classical fractals - the Cantor set, the Sierpiński triangle and carpet, the Koch curve and snowflake, Pythagorean tree, the Julia set and the Mandelbrot set. For every of them is described their feature of self-similarity and is calculated their self-similarity dimension that differs from term of dimension we know.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:397648
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-07-02 11:51:59