Mutations that affect pattern formation in the zebrafish have been widely studied over the past few decades, leading to speculations as to the mechanism by which stripes, spots and other skin patterns are formed. Recent in silico developments in modeling of cellular dynamics now permit explicit analysis of how cells migrate and interact, and we describe here an in silico simulation that appears to reproduce many of the surface patterns previously reported in zebrafish. We find that many observed zebrafish patterns are necessarily associated with expression of repulsive as well as attractive cellular ligands, and we make predictions for the detailed effects of changes in expression of these ligands.