Dev Genes Evol (2011) 221:255–279 to study regeneration and self-regulation. In 1971, Hans Meinhardt, who had also received a Ph.D. in physics, joined the group. Influenced by ideas from cybernetics, they formulated their theory of local self-activation and lateral inhibition. From work in the neighbouring institute of Biological Cybernetics, they were aware that during contrast enhancement in the visual system, a local activa- tion by the stimulus is linked to an inhibitory effect in the surroundings (Kirschfeld and Reichardt 1964). The external stimuli provide a pattern, which is enhanced through lateral inhibition. Inhibitory processes had also been invoked in developmental biology (Spiegelman 1945; Rose 1952). Also here, like in the sensory system, they could account for the spatial refinement of an inhomogeneous starting situation. However, in experiments with hydra, the Gierer group had observed axis formation emerging from a uniform aggregate of cells lacking an apparent prepattern. How could one explain such a situation? Inspiration came again from the context of cybernetics. In an account of the intellectual roots of their theory, Meinhardt and Gierer (2000) cite the work of Maruyama (1963), who was stressing the importance of positive feedback in nature and society. He pointed out that classical cybernetics was primarily concerned with deviation-counteracting feedback networks, like thermostats. However, many processes in the universe from the weathering of rocks, the fixation of single mutations in a population, to the growth of cities and economic inequality represent deviation-amplifying sys- tems. They are governed by positive instead of negative feedback. Maruyama envisages a ‘second cybernetics’ in which deviation-amplifying processes are of central impor- tance. Positive feedback provides the ingredient which causes a self-organising process to start. By combining a local deviation-amplifying process with lateral inhibition, Gierer and Meinhardt could explain how structure forma- tion was possible starting from a homogeneous state. Lateral inhibition was realised either through substrate depletion by the local activation process or by the production of an inhibitor. Key aspects of the kinetics were non-linear autocatalysis of the activator and, as in Turing’s model, differences in the diffusion rates of the components. The short-range action of the activator resulted from a small diffusion constant, the long-range effect of substrate depletion or inhibitor action resulting from a large diffusion constant. When they submitted their first paper (Gierer and Meinhardt 1972), they had not read Turing’s work. A referee of the paper pointed out its existence (Meinhardt 2006). It is important to note the differences between Turing’s approach and that of Gierer and Meinhardt. Firstly, the demonstration that chemical kinetics is sufficient to produce a spatial pattern from uniformity was not their main goal. They rather formulated two principles which in 265 conjunction are sufficient for self-organised patterning. The molecular or cellular realisation was left open. ‘The formalism of the theory is consistent with many…inter- pretations… Thus, production of components may be due to synthesis or release; removal to degradation or leakage; spreading to diffusion, convection, mechanisms involving transport along intracellular or intercellular fibres, and/or transducing effects across membranes. It is not adequate to limit considerations to molecular diffusion. What matters is that activation and inhibition effects spread from the place of origin in an attenuated manner’ (Gierer 1981). Thus, the frequent characterisation of the Gierer–Meinhardt model as a chemical-reaction-diffusion theory is not entirely correct. Molecular kinetics and normal diffusion just provided the simplest case for writing down the equations. Secondly, and most importantly, Gierer and Meinhardt showed that their theory could account for self-regulation and scaling even if they used only straightforward molecular kinetics. A simple restriction of the amount of activator which can be produced locally, e.g. by introducing a saturation term, leads to size regulation. Thus, the criticism that reaction-diffusion equations can only produce static chemical waves was not justified. The most important dynamic phenomenon in developmental biology was perfectly in the range of the theory. Had Driesch seen the dynamic aspect of Meinhardt’s simulation, which by now could be followed easily at the computer, I suggest, he would have given up his vitalistic views. Third, in contrast to Turing, Gierer and Meinhardt had a concrete experimental system in mind, the regeneration behaviour of hydra (Gierer, et al. 1972). Therefore, they introduced a number of features that were specifically derived from their experimental results, such as source densities which are influenced by the activator–inhibitor system, but change with different time scales. Their reference list contains 21 papers, almost half of them (10) dealing with hydra. In the subsequent years, it was Hans Meinhardt in particular who extended the models and applied them to almost every dynamical problem in developmental biology. This resulted in his monograph Models of biological pattern formation (Meinhardt 1982), in which a bewilder- ing multitude of complex phenomena from developmental biology were treated with clear analytical concepts. The work was much more than a stereotypic application of the idea of local activation and lateral inhibition. Meinhardt tried to work out the developmental logic underlying experimental findings and tested the validity of his ideas by computer simulations. Three examples might suffice to exemplify this point. First, in 1976, French and Bryant had formulated the polar coordinate model for appendage patterning (French, et al. 1976). This model worked with circumferential positional values, a shortest intercalation