The occurrence of spatially ordered structures plays an important role in biology (examples: morphogenesis, ecosystems, dynamics of populations, etc.). Turing proposed a reaction-diffusion process that is the basis for most theoretical studies of stationary biological pattern formation. Now, when Turing structures are obtained in experiments (40 years after Turing's publication), it is interesting to discover whether Turing structures are the only mechanism used by nature in biological pattern formation. In microbial growth, we have found experimental evidence of an alternative to the Turing model that is based on waves displayed in excitable media. In studies of Escherichia coli populations, we observed that interacting taxis waves create motionless patterns. Taxis waves consuming two different substrates (serine and aspartic acid) were involved. Taxis waves consuming serine stop when they collide. However, those supported by consumption of aspartic were initiated at the collision line. Colliding and annihilating in turn, the waves give rise to stationary patten formation, and wave theory provides an alternative to the classical Turing mechanism.