2940 KB67 KB201420242023Simčič, Lukaletnik:10številka:228 str.COBISSID_HOST:166308867ISSN:2385-8567URN:URN:NBN:SI:doc-DGYZ658NslZaložba Fakultete za matematiko in fiziko Univerze v LjubljaniMatrikafilled Julia setsnapolnjene Juliajeve množiceregular functionsregularne funkcijerepresentation formulareprezentacijska formulaKvaternionska regularna iteracija|The main goal of the work is the description and visualization of filled Julia sets for some regular quaternion functions. A criterion is described for unboundedness of orbits and filled Julia sets of polynomials with coefficients from one slice ?$\mathbb{C}_I$? are described. Their intersection with the plane ?$\mathbb{C}_I$? coincides with the already known complex filled Julia set and the intersection with the other planes is thereby precisely determined. Code for computing with regular functions in Mathematica is also attached and described, as well as an effective algorithm for computing orbits of regular functionsGlavni cilj dela je opis in vizualizacija napolnjenih Juliajevih množic za nekatere regularne kvaternionske funkcije. Izpeljan je kriterij za neomejenost orbit ter opisane so napolnjene Juliajeve množice za polinome z vsemi koeficienti iz ene rezine ?$\mathbb{C}_I$? . Njihov presek z ravnino ?$\mathbb{C}_I$? sovpada z že znano kompleksno napolnjeno Juliajevo množico, presek z ostalimi ravninami pa je s tem natanko določen. Priložena in opisana sta tudi koda za računanje z regularnimi funkcijami v Mathematici in efektiven algoritem za računanje orbit regularnih funkcijTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of Slovenia