Izbrane teme sodobne fizike in matematike
Glavni 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 nekatere razrede regularnih polinomov, na primer takih, katerih vsi koeficienti so iz iste razine. Njihov presek s to rezino 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 funkcij.
The main goal of this work is to describe and visualize filled Julia sets for certain regular quaternionic functions. A criterion for the unboundedness of orbits is derived and filled Julia sets for certain classes of regular polynomials are described, for example, for those with all the coefficients from the same slice. Their intersection with this slice coincides with the already known complex filled Julia set and the intersection with 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 functions.