Current interest in pattern formation can be traced to a seminal paper by Turing, who demonstrated that a system of reacting and diffusing chemicals, called morphogens, can interact so as to produce stable nonuniform concentration patterns in space. Recently, a Turing model has been suggested to explain the development of pigmentation patterns on species of growing angelfish such as Pomacanthus semicirculatus, which exhibit readily observed changes in the number, size, and orientation of colored stripes during development of juvenile and adult stages, but the model fails to predict key features of the observations on stripe formation. Here we develop a generalized Turing model incorporating cell growth and movement, we analyze the effects of these processes on patterning, and we demonstrate that the model can explain important features of pattern formation in a growing system such as Pomacanthus. The applicability of classical Turing models to biological pattern formation is limited by virtue of the sensitivity of patterns to model parameters, but here we show that the incorporation of growth results in robustly generated patterns without strict parameter control. In the model, chemotaxis in response to gradients in a morphogen distribution leads to aggregation of one type of pigment cell into a striped spatial pattern.The coupling between growth and patterning, which is important in many developing systems (1-3), is particularly evident in the coloration patterns of the angelfish Pomacanthus (Fig. 1). Young angelfish of this genus display three vertical white stripes on a dark blue/black background, and as the fish grows, new stripes develop via gradual insertion between the preexisting stripes. This process repeats twice before the pattern undergoes a further transformation into its adult form. The first workers to suggest a mechanistic explanation for stripe doublings were Kondo and Asai (4), who proposed a Turing model (5) that predicts regular doubling of the number of morphogen peaks on a growing one-dimensional domain. Although their predictions are qualitatively consistent with the patterning sequence in the angelfish, there are several important observations that are not explained (6). In vivo, new stripes emerge gradually between preexisting stripes, first appearing faint and narrow, and then slowly widening, and the mature stripes are narrow in comparison with the region separating them. In contrast, the Kondo-Asai model predicts that the width of new stripes is nearly equal to that of mature stripes, and narrow stripes can only be obtained by choosing a threshold close to the peak of morphogen concentration, in which case stripe formation is unlikely to be robust to parameter variations. Furthermore, it is not known whether the one-dimensional peak doublings translate to two-dimensional stripe doublings. A Turing model on a geometrically realistic two-dimensional domain has been considered (7), but this model contains boundary sources that orient the pattern, in the absence of which only spo...