We use theory and experiment to investigate the interaction between the evolution of conflict, and emergent patterns in a concrete system: bacterial biofilms. Our model predicts that a common set of physical processes underlie both natural selection for competition (evolutionary conflict) and the generation of higher order patterns in biofilms (self-organization). We find that a combination of processes of physical pushing and nutrient competition generates nutrient-dependent Turing patterns. We develop a simple empirical assay that systematically varies the amount of nutrients available to cells, which shows the predicted correlation between the patterns and nutrient availability. Finally, we use our simulations to show that there can be an important interaction between the evolution of conflict in biofilms and pattern formation. In particular, we show that selection can favor energetically-costly spreading strategies that simultaneously reduce biofilm productivity and disrupt patterns.