Dev Genes Evol (2011) 221:255–279 reaction scheme is physically unrealistic because of the trimolecular step’ and that it was mainly chosen for mathematical reasons. Because of its simplicity, the Brusselator is indeed still used as an example in mathe- matical treatments of pattern formation theory (Cross and Greenside 2009). As Prigogine and Lefever (1968) point out, systems with higher number of components can be devised easily that are based on more realistic kinetics and show limit cycle oscillations. In particular, enzyme kinetics offered a rich source for non-linear reaction schemes. In an influential paper, the new ideas on dissipative structures were applied to biological questions (Prigogine, et al. 1969). Albert Goldbeter, one of the authors of this paper, would become a leading figure in the analysis of rhythmic phenomena in biology (Goldbeter 1996). Nevertheless, at the end of the 1960s there was no single case of an experimentally validated mechanism for an oscillating reaction (or a reaction producing spatial pat- terns). However, the theoretical work provided a strong motivation for experimental approaches. The Brussels school contributed to popularising the BZ reaction as the best experimental example of a chemical oscillator and motivated chemists to do research on its mechanism. In the early 1970s, R. Field and E. Körös in the laboratory of R. Noyes at the University of Oregon undertook a systematic investigation of the BZ reaction. When they started, the option was still discussed that the oscillatory behaviour and the chemical wave patterns were due to heterogeneous effects and would not occur in a completely homogeneous phase. Obviously, the concept of large-scale coherent phenomena far from equilibrium was still not easy to grasp for physical chemists. In 1972, Field, Körös and Noyes published the first successful and largely complete kinetic model of the BZ reaction which later was called the FKN (Field, Körös, Noyes) mechanism (Field, et al. 1972). To explain the oscillatory behaviour, they distinguished ten different reactions represented by detailed kinetic equations. From these, they later derived a model capturing the core kinetics which included only three variables for compo- nents and five equations (Field and Noyes 1974). This model was extensively used for computer simulations and largely reproduced the quantitative data from experiments. In analogy to the Brusselator, it was dubbed the Oregona- tor. Among biologists, the BZ reaction became very popular through the work of Arthur Winfree who, in particular, was interested in the mechanism of spiralwave formation (Winfree 1972). Taken together in the early 1970s, both theoretical and experimental approaches had provided a thorough under- standing of the spontaneous formation of order in homo- geneous chemical systems. The Brussels school played a major role in clarifying the compatibility of these phenom- ena with the laws of thermodynamics and in defining the 261 general prerequisites for self-organised patterning. The attempt to derive functions for entropy production which characterise temporal or spatial pattern formation far from equilibrium was later criticised (Landauer 1975) and does not play any role in modern treatments of this subject (Cross and Hohenberg 1993; Cross and Greenside 2009). It also should be noted that parallel to the Brussels school, which focused on chemistry, several groups studied the formation of ordered states in purely physical non- equilibrium systems. Hermann Haken developed his theory of synergetics based on his earlier work on laser theory (Haken 1977). The most impressive link between theory and experiments was probably achieved in studies of hydrodynamic phenomena (Swift and Hohenberg 1977; Cross and Hohenberg 1993). Ironically, Prigogine’s hope for a deeper understanding and extension of non-equilibrium thermodynamics was not fulfilled by studying collective phenomena of self-organisation at the mesoscopic or macro- scopic level, but rather through theories and experiments addressing single molecule behaviour at the nanoscale (Jarzynski 2011). Biology is providing prime examples also for these new approaches (Collin et al. 2005). Early theories of biological pattern formation Despite the obvious interest of the Brussel’s school in biology, its main goal was an extension of thermodynamics for which biology merely provided some of the nicest examples and applications. Most of the papers of the Brussels school addressed physicists and were not directly inspired by biological questions. However, in the meantime two papers had appeared, which were entirely motivated by problems of biological pattern formation. In 1952, Alan Turing had published The chemical basis of morphogenesis which, as already pointed out, was important for Prigo- gine’s early work on dissipative structures (Prigogine and Nicolis 1967). However, Turing was not concerned with problems of chemistry or thermodynamics. Rather, he immediately addressed particular biological questions. Why was he interested in this topic at all? Before working on mathematical biology, Turing had made major contri- butions to mathematical logic, cryptology, computer sci- ence and artificial intelligence (Hodges 1992). None of these projects, with the exception of the last one, had links to the life sciences. However, Turing had kept a vivid interest in biology throughout his life (Saunders 1993). As a young boy, an American children’s book Natural wonders every child should know (Brewster 1912) had stimulated his interest in science. This book is devoted entirely to living nature and contains detailed information about animal and plant development, reproducing many figures from original publications. These include accounts of chicken and frog