Kvaternionska regularna iteracija - Simčič, Luka (Matrika, 2023)
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 functions.
Keywords: filled Julia sets; napolnjene Juliajeve množice; regular functions; regularne funkcije; representation formula; reprezentacijska formula