A global approach to botanic patterns

A simple model of the controlled growth of botanic patterns is analysed. Each new-born sprout emerging on the apical ring is associated with a local burst of some (chemical) phenomenon which inhibits the rise of further sprouts, except in the region where this inhibition is minimal. It is shown that the algebraic value of the divergence thus issued strongly depends on the global properties of the functions used in the description of the model. According to the convexity properties of these functions, the divergence tends to assume either irrational or rational values. “Simple” rational values are only excluded when the concentration of the inhibiting phenomenon may be represented by some sharp peaked functions. Algebraic properties of the divergence may be considered not as the consequence of a precise growth mechanism but merely as a statistical consequence of the distribution of the inhibition.