During morphogenesis in the slime mold Polysphondylium pallidum, spherical masses of cells called whorls pinch off from the slug at regular intervals. Soon afterward, branches form at equidistant positions around the whorl equator. We have quantified the relationship between the number of cells in a whorl, and the number of branches that form. We find that the number of branches produced is proportional to the surface area of the whorl, suggesting that the patterning process is confined to the whorl surface. This observation is consistent with theoretical arguments that mechanisms for pattern formation would likely operate in one or two dimensions, not three.