A concentric pulse by motile cells of Escherichia coli (E. coli) propagates and the cells aggregate to form self-organized patterns.We summarize experimental and numerical results on the self-organized pattern formation of E. coli to elucidate some aspects of its mechanism. Our presentation includes experiments on E. coli patterns, as well as numerical simulations on the basis of a reaction-diffusionchemotaxis model.We find good agreement for one-dimensional propagating fronts in observation and simulation. However, corresponding results for two-dimensional circular bacterial clusters have still not been obtained.