Feathers are complex, branched keratin structures that exhibit a diversity of pigmentation patterns. Feather pigments are transferred into developing feather keratinocytes from pigment cells that migrate into the tubular feather germ from the dermis. Within-feather pigment patterns are determined by differential pigmentation of keratinocytes within independent barb ridges during feather development. Little is known about the molecular mechanisms that determine which keratinocytes receive pigment. We apply reaction-diffusion models to the growth of within-feather pigment patterns based on a realistic model of feather growth. These models accurately simulate the growth of a diversity of the within-feather pigmentation patterns found in real feathers, including a central patch, a 'hollow' central patch, concentric central patches, bars, chevrons, a central circular spot, rows of paired spots, and arrays of offset dots. The models can also simulate the complex transitions between distinct pigmentation patterns among feathers observed in real avian plumages, including transitions from bars to chevrons, bars to paired dots, and bars to arrays of dots. The congruence between the developmental dynamics of the simulated and observed feather patterns indicates that the reaction-diffusion models provide a realistic and accurate description of the determination of pigment pattern within avian feather follicles. The models support the hypothesis that within-feather pigmentation patterning is determined by antagonistic interactions among molecular expression gradients within the tubular follicle and feather germ.