Many authors consider that the mechanisms of pre–pattern formation constitute one of the most important aspects of morphogenetic phenomena. For example, Edwards (1982) and Hermant (Section 3.4.2) produced phyllotactic pre–patterns using projective geometry and topology, respectively. Many theories propose that the site of organ formation is determined by a chemical pre–pattern, generated by a diffusion–reaction mechanism. By pre–pattern is meant in this appendix the establishment of a concentration gradient of substances from an almost equal initial distribution. In this context the patterns observed in organisms are considered to be the results of the interaction of their constituents such as cells, genes, or molecules. One of the models that has received the utmost attention is the one by Gierer and Meinhardt (see these authors in the Bibliography). The model is based on a principle of formation of patterns by a process of molecular activation and inhibition. Activation is an autocatalytic process with short spatial range, whereas inhibition is considered to be a comparatively long–range interaction in order to ensure stability of the developing structures. We have seen in Section 8.6.2 that Richter and Schranner (1978) used this model. Berding, Harbich and Haken (1983) used it to generate pre–patterns of capituli and leafy stems.

In order to better understand the principle, Meinhardt (1984) proposes the following analogy. A river can be formed from a minor depression in the landscape. Raindrops accumulate, erosion is accelerated, and a larger quantity of water rushes towards the newly created valley.