Turing Patterns

In the first chapter of this book, we noted the “dark age” of nearly forty years separating the work of Bray and Lotka in the early 1920s and the discovery of the BZ reaction in the late 1950s. Remarkably, the history of nonlinear chemical dynamics contains another gap of almost the same length. In 1952, the British mathematician Alan Turing wrote a paper in which he suggested that chemical reactions with appropriate nonlinear kinetics coupled to diffusion could lead to the formation of stationary patterns of the type encountered in living organisms. It took until 1990 for the first conclusive experimental evidence of Turing patterns to appear (Castets et al., 1990). Turing was a formidable figure (Hodges, 1983). He was responsible for much of the fundamental work that underlies the formal theory of computation, and the notion of a “Turing machine” is essential for anyone who wishes to understand computing and computers. During World War II, Turing was a key figure in the successful effort to break the Axis “Enigma” code, an accomplishment that almost certainly saved many lives and shortened the war in Europe. His 1952 paper, entitled “The Chemical Basis of Morphogenesis” was his only published venture into chemistry, but its impact has been enormous. Recently, this classic paper has been reprinted along with some of Turing's unpublished notes on the origins of phyllotaxis, the arrangement of leaves on the stems of plants (Saunders, 1992). In this chapter, we shall describe the nature of Turing patterns and some of the systems in which they may play a role, explore why they have been so elusive, examine the experimental systems in which they have been demonstrated, and consider other systems and other methods for generating them. Much of our discussion will focus on the chlorite-iodide-malonic acid (CIMA) reaction in which the patterns were first seen. In the study of Turing patterns, the CIMA system and its relatives play much the same role today that the BZ reaction played during the 1960s and 1970s in the study of chemical oscillation.