Evolutionary genetic studies have uncovered abundant evidence for genomic hotspots of phenotypic evolution, as well as biased patterns of mutations at those loci. However, the theoretical basis for this concentration of particular types of mutations at particular loci remains largely unexplored. In addition, historical contingency is known to play a major role in evolutionary trajectories, but has not been reconciled with the existence of such hotspots. For example, do the appearance of hotspots and the fixation of different types of mutations at those loci depend on the starting state and/or on the nature and direction of selection? Here we use a computational approach to examine these questions, focusing the anthocyanin pigmentation pathway, which has been extensively studied in the context of flower color transitions. We investigate two transitions that are common in nature, the transition from blue to purple pigmentation and from purple to red pigmentation. Both sets of simulated transitions occur with a small number of mutations at just four loci and show strikingly similar peaked shapes of evolutionary trajectories, with the mutations of largest effect occurring early but not first. Nevertheless, the types of mutations (biochemical vs. regulatory) as well as their direction and magnitude are contingent on the particular transition. These simulated color transitions largely mirror findings from natural flower color transitions, which are known to occur via repeated changes at a few hotspot loci. Still, some types of mutations observed in our simulated color evolution are rarely observed in nature, suggesting that pleiotropic effects further limit the trajectories between color phenotypes. Overall, our results indicate that the branching structure of the pathway leads to a predictable concentration of evolutionary change at hotspot loci, but the types of mutations at these loci and their order is contingent on the evolutionary context.