Modeling and visualization of leaf venation patterns

Modeling and visualization of leaf venationpatternsAbstractWe introduce a class of biologically motivated algorithms for generating leaf venationpatterns. These algorithms simulate the interplay between three processes: (1) development ofveins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of thehormone source distribution by the proximity of veins; and (3) modification of both the veinpattern and source distribution by leaf growth. These processes are formulated in terms ofiterative geometric operations on sets of points that represent vein nodes and auxin sources.

2.2 Mathematical description of leaf growth. The development of venation patterns is correlated with the growth of leaf blades. Growth can be characterized by the growth ten- sor field [Hejnowicz and Romberger 1984], which specifies the magnitude of the expansion of infinitesimal surface regions in var-

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  Modeling, Patterns, Leaf, Visualization, Modeling and visualization of leaf venation patterns, Venation, Of leaf, Venation patterns

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