The main goal of this work is the description and the visualization of filled Julia sets for quaternionic quadratic polynomials of a quaternionic variable which are a generalization of the known filled Julia sets for complex quadratic polynomials of a complex variable. A criterion is described for unboundedness of orbits and filled Julia sets of a certain class of polynomials are described. Their intersection with two specific planes coincides with the already known complex filled Julia sets 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 iterative algorithm for computing orbits of regular functions.
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