Motivating biological example and model. (a) Wild-type zebrafish feature stripe patterns in their skin. These patterns consist of several types of brightly colored pigment cells. (b) Over the course of a few months, these cells organise sequentially into stripes and interstripes from the centre of the fish body outward. (c) For the purposes of this manuscript, we focus on a single population of black melanophores or gold dense xanthophores, using a simplified version of the model from (Volkening et al., J Roy Soc Interface, 2015). The agent-based model (ABM) that motivates our work describes how patterns arise through cell differentiation, competition, and movement. In our simplified version of the ABM, we assume new cells appear at randomly selected locations based on short-range activation; this models cell differentiation from uniformly distributed precursors (red position), and we also refer to this as "proliferation" or "birth" in this paper. (We describe the cell-differentiation rules in the full model in more detail in Supplementary Fig.~1.) In both our work and the ABM, cell movement is governed by ordinary differential equations (ODEs). (d) These ODEs account for cell--cell repulsion through potential functions, which describe melanophore--melanophore (Wmm) and xanthophore--xanthophore (Wxx) interactions as a function of their pairwise distance r. Red scale bar is250 micrometres (um) in (b). Image (a) adapted from Fadeev et al. (eLife, 2015) and licensed under CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Image (b) adapted from Frohnhofer et al. (Development, 2013) and licensed under CC-BY 3.0 (https://creativecommons.org/licenses/by/3.0/); published by The Company of Biologists Ltd.