A large variety of regular and irregular spatio-temporal patterns may form when chemical reactions are coupled with transport processes (diffusion, hydrodynamic flow). The patterns evolve and prevail under conditions far from thermodynamic equilibrium in that there is continuous influx of physical or chemical energy. Due to this openness, they are considered model cases for living systems in biology. The dynamics of pattern evolution is governed by nonlinear interactions. In spatial concentration distributions, several geometrical shapes predominate. Their structural elements are singular points, branching points, bands, circles, spirals, helices. These elements and compositions thereof are also found in biology. The authors discuss the significance of regulatory principles in the creation of spatial complexity, which often reveal remarkable aesthetic aspects.