Linearni operatori i geometrijske transformacije u ravnini i prostoru s primjenama na fraktalne skupove

undergraduate thesis

• Title (english): Linear operators, geometric transformations in plane and space with applications to fractal sets
• Author: Mate Buljan
• Mentor: Neven Elezović (mentor)
• Committee member: Neven Elezović (predsjednik povjerenstva)
• Committee member: Tomislav Burić (član povjerenstva)
• Committee member: Andrea Katarić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2018-07-13, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

U ovom radu su proučene linearne transformacije u ravnini i prostoru te načini generiranja fraktalnih skupova koji se opisuju pomoću linearnih transformacija. Promatrana su dva algoritma generiranja IFS fraktala te je više primjera obrađeno na način da je opisana njihova konstrukcija te potrebne linearne transformacije, izračunata je fraktalna dimenzija te neke od njihovih varijacija. Pokazan je nedostatak determinističkog algoritma na primjeru Barnsleyeve paprati te su na tom istom primjeru opisane obje verzije slučajnog algoritma. Opisan je i postupak dobivanja fraktalnih plamenova. Napravljena je aplikacija za prikaz geometrijskih transformacija u ravnini te je implementiran slučajni algoritam za generiranje IFS fraktala.

Abstract (english)

In this paper we studied linear transformations in plane and space and ways of generating fractal sets which use linear transformations. Two algorithms for generating IFS fractals are described and number of examples are analysed such that the description of their construction is given, linear transformations needed for their construction are described, fractal dimension is calculated and some of their variations are mentioned and also described. Lack of efficiency of deterministic algorithm is shown on the example of Barnsley's fern which was also used to describe both versions of random algorithm. The procedure for generating fractal flames is also given. Simple application for displaying geometric transformations and random algorithm for generating IFS fractals is made.

• Keywords: IFS; generiranje fraktala; slučajni algoritam; deterministički algoritam
• Keywords (english): IFS; generating fractal images; deterministic algorithm; random algorithm; fractal flames
• Language: croatian
• URN:NBN: urn:nbn:hr:168:086488
• Study programme: Title: Computing; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2019-03-13 19:27:20