In biological development, the generation of shape is preceded by the spatial localization of growth factors. Localization, and how it is maintained or changed during the process of growth, determines the shapes produced. Mathematical models have been developed to investigate the chemical, mechanical and transport properties involved in plant morphogenesis. These synthesize biochemical and biophysical data, revealing underlying principles, especially the importance of dynamics in generating form. Chemical kinetics has been used to understand the constraints on reaction and transport rates to produce localized concentration patterns. This approach is well developed for understanding de novo pattern formation, pattern spacing and transitions from one pattern to another. For plants, growth is continual, and a key use of the theory is in understanding the feedback between patterning and growth, especially for morphogenetic events which break symmetry, such as tip branching. Within the context of morphogenetic modelling in general, the present review gives a brief history of chemical patterning research and its particular application to shape generation in plant development.

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