Following the success of the reaction-diffusion models for chemical and biological morphogenesis, successive generalizations were reported in various works. The wave-diffusion models were based on the foundational work of mathematical physics, the wave equation for the vibrating string of d'Alembert, published in 1749. An early model of this type was the one-dimensional lattice of oscillators of Fermi, Pasta, and Ulam, in which chaotic behavior was observed in the 1950s. A very general model of this type is the cellular dynamical system discussed in the 1970s in my book, Cellular Dynamata.