We have quantitatively modeled heterocyst differentiation after fixed nitrogen step-down in the filamentous cyanobacterium Anabaena sp. PCC 7120 without lateral inhibition due to the patterning proteins PatS or HetN. We use cell growth and division together with fixed-nitrogen dynamics and allow heterocysts to differentiate upon the local exhaustion of available fixed nitrogen. Slow transport of fixed nitrogen along a shared periplasmic space allows for fast growing cells to differentiate ahead of their neighbors. Cell-to-cell variability in growth rate determines the initial heterocyst pattern. Early release of fixed nitrogen from committed heterocysts allows a significant fraction of vegetative cells to be retained at later times. We recover the experimental heterocyst spacing distributions and cluster size distributions of Khudyakov and Golden [Khudyakov, I.Y., Golden, J.W., 2004. Different functions of HetR, a master regulator of heterocyst differentiation in Anabaena sp PCC 7120, can be separated by mutation. Proc. Natl. Acad. Sci. U. S. A. 101, 16040-16045].