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We demonstrate how the choice of Monte Carlo algorithm, strength of external field, and random anisotropy variations strongly determine simulated kinetics and influence the resulting form and connectivity of magnetic domains. Particular forms of anisotropy distributions are shown to have different effects on domain pattern formation, and the dependence of the pattern characteristics on the strength of the applied reversing field is determined. For example, the kinetics for typical magnetooptic materials at low reversal field strengths is governed by individual site nucleation and domain growth. At high field strengths, very different patterns are observed. The pattern shapes and characteristics are clearly distinguished through the use of Minkowski functional analysis and illustrate the power of this method.