3. Reaction-diffusion models.

The evolution of mathematical models for morphogenesis began in 1924, with the work or Roland Fischer. This was the first example, to my knowledge, of a reaction-diffusion equation. This type of model combines a spatially distributed chemical reaction with a diffusion of the chemical reactants through the spatial substrate. After intuitive and theoretical discussions of this sort of model for embryogenesis (by Rashevsky, the founder of mathematical biology, in the 1930s) and for plant phyllotaxis (by Turing in England in the 1950s) the computer simulations began in the 1970s, in the group of Prigogine in Brussels. These simulations proved conclusively that the reaction-diffusion models were capable of morphogenesis, and many more studies have followed (see the books of Murray and Meinhardt in the Bibliography).

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|| 1. Introduction || 2. Vibrations and morphogenesis || 3. Reaction-diffusion models || 4. Wave-diffusion models || 5. Simulation results || 6. Conclusion || Acknowledgments/Bibliography