262 embryology, descriptions of starfish and planarian regener- ation and examples of twinning and homeotic transforma- tions, directly taken form Bateson’s influential Materials for the study of variation (1894). In the 1930s, Turing had read D’Arcy Thompson’s On growth and form and was particularly fascinated with the fact that leaf-arrangements (phyllotaxis) frequently follow the Fibonacci series. After the war, he decided to work on the construction of an electronic computer. He called this project ‘building a brain’. In 1948, he wrote his first article on problems of artificial intelligence, which contains remarks on the relation between genes and brain structure (reprinted in Copeland 2004, 410–432). In the same year, he moved to Manchester where he played an important role in building one of the first computers able to perform massive calculations. He continued his philosophical reflections on the relation between human mind and computer (Turing 1950) and became involved in discussions with Michael Polanyi, a physicochemist turned philosopher who held a chair in social studies at Manchester. Polanyi criticised reductionist approaches not only regarding the human mind, but also for biology in general. For example, he claimed that morphogenesis cannot fully be explained on mathematical grounds (Roth 2011b). This might have provided additional incentives for Turing to formulate a mathematical theory of morphogenesis. However, his main motivation certainly was the aware- ness that the relation between genetic information and morphology represented one of the central unsolved problems in biology. He clearly states that ‘the purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organisms’ (Turing 1952, 37). The genes are presumed to act purely as catalysts and ‘influence the anatomical form of the organism by determining the rates of those reactions which they catalyse’ (Turing 1952, 38). In describing the zygote, the early embryo or any developing tissue Turing initially takes chemical and mechanical properties of the cell into account. He omits only electrical properties and the internal structure of the cell because of insurmountable problems with complexity. However, also the ‘interdependence of the chemical and mechanical data adds enormously to the difficulty’ so that the paper then focuses on cases where ‘the mechanical aspect can be ignored and the chemical aspect is the most significant’ (ibid). This also provides a closer link to the primary action of the genes which he thought to be chemical. Turing then assumes the existence of ‘chemical substances, called morphogens, reacting together and diffusing through a tissue’. These are initially uniformly distributed, but by virtue of their interactions, become distributed in spatial patterns. In a second step, these unequally distributed morphogens activate reactions in the Dev Genes Evol (2011) 221:255–279 tissue which produce the real shape. The word ‘morphogen’ was chosen by Turing ‘to convey the idea of a form producer’ (ibid). He compares his morphogens with Waddington’s evocators, substances which induce the formation of a particular organ, and suggests that it is legitimate to separate the processes which lead to a particular ‘distribution of the evocator in space and time’ from the ‘reactions set in train by it’. Here, Turing presages an idea, which later would become very important through the work of Lewis Wolpert, the separability of pattern formation and cell differentiation/morphogenesis. With his paper, Turing wanted to reach a broad spectrum of readers including, in particular, biologists. Therefore, he uses sections 2 and 3 to provide the background of some mathematics and chemistry and in section 4 he presents his main idea: ‘the break down of symmetry and homogeneity’ in a system of interacting and diffusing chemicals, at a very elementary level. He chooses only two cells and two chemicals X and Y. The production of X depends on X itself (autocatalysis), while the production of Y depends on X (cross-catalysis). In addition, X moves slower than Y to the neighbouring cell, i.e. the diffusion rate of X is smaller than that of Y. The numerical values of the reaction constants and diffusion rates are chosen such that everybody can do the calculations by hand. Turing shows then that this system has an unstable homogenous equilibrium. It will accentuate any small differences in X and Y which may occur between the two cells just on the basis of random fluctuations. The final state will always be a stable difference of X and Y concentrations between the two cells, i.e. a stable pattern in space. Turing’s deep concern about problems of real biology is apparent from his digression into left-right asymmetry (section 5) before he enters into a serious mathematical analysis of his reaction-diffusion model. The occurrence of left–right asymmetric organisms can be explained as the result of an early event of symmetry breaking. However, left-handed and right-hand organisms should occur with equal frequencies since the laws of physics and chemistry underlying his reaction-diffusion theory do not possess an intrinsic preference for left- or right-handedness. Turing admits that the prevalence of only one type of handedness in a given species poses a serious problem for his model. He sees, however, one possible solution; the early symme- try breaking processes might be influenced by the handed- ness of organic molecules present in the embryo. Within modern developmental biology left–right asymmetry in- deed remained enigmatic for a long time. Only recently has it become clear that for vertebrates, the symmetry-breaking step depends, as Turing suggested, on the chirality of a macromolecular complex (the cilium) which influences a reaction-diffusion mechanism (Tabin 2006).