Most theories of phyllotaxis are based on the idea that the formation of new primordia is inhibited by the proximity of older primordia. Several mechanisms that could result in such an inhibition have been proposed, including mechanical interactions, diffusion of a chemical inhibitor, and signaling by actively transported substances. Despite the apparent diversity of these mechanisms, their pattern-generation properties can be captured in a unified manner by inhibition fields surrounding the existing primordia. In this paper, we introduce a class of fields that depend on both the spatial distribution and the age of previously formed primordia. Using current techniques to create geometrically realistic, growing apex surfaces, we show that such fields can robustly generate a wide range of spiral, multijugate, and whorled phyllotactic patterns and their transitions. The mathematical form of the inhibition fields suggests research directions for future studies of phyllotactic patterning mechanisms.
Richard S. Smith, Cris Kuhlemeier, and Przemyslaw Prusinkiewicz: Inhibition fields for phyllotactic pattern formation: a simulation study. Canadian Journal of Botany 84 (11), pp. 1635-1649, 2006.
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