As a model system to study physical interactions in multicellular systems, we used layers of Escherichia coli cells, which exhibit little or no intrinsic coordination of growth. This system effectively isolates the effects of cell shape, growth, and division on spatial self-organization. Tracking the development of fluorescence- labeled cellular domains, we observed the emergence of striking fractal patterns with jagged, self-similar shapes. We then used a large-scale, cellular biophysical model to show that local instabilities due to polar cell-shape, repeatedly propagated by uniaxial growth and division, are responsible for generating this fractal geometry. Confirming this result, a mutant of E. coli with spherical shape forms smooth, non-fractal cellular domains. These results demonstrate that even populations of relatively simple bacterial cells can possess emergent properties due to purely physical interactions. Therefore accurate physico-genetic models of cell growth will be essential for the design and understanding of genetically programmed multicellular systems.