Mathematical modeling based on first principles quantifies tumor growth dependence on interactions between a set of variables including genomic instability producing variations in sub-tumor clonal expansion and generating nutrient diffusion gradients and demonstates that these determinants of heterogeneity, and not angiogenesis per se, conspire to produce the typical morphologic patterns of infiltrative tumor boundaries in histopathology. We demonstrate that heterogeneity in sub-tumor clonal expansion and nutrient consumption drives migration and proliferation of the emerging more aggressive clones up a nutrient concentration gradient within and beyond the central tumor mass. This heterogeneity and loss of cell adhesion trigger a gross morphologic instability that leads to replacement of less aggressive clones and separation of tumor cell strands or clusters infiltrating into adjacent tissue. This model allows all variables that characterize the biophysics of tumor growth to be considered and could be applied to determine the probabilistic behavior of tumors given their pathologic appearance.