Simulation and visualization of adapting venation patterns

Abstract

This paper suggests a procedural biologically motivated method to simulate the development of leaf contours and the generation of different levels of leaf venation systems. Leaf tissue is regarded as a viscous, incompressible fluid whose 2D expansion is determined by a spatially varying growth rate. Visually realistic development is described by a growth function relative elementary growth rate that reacts to hormone (Auxin) sources embedded in the leaf blade. The shape of the leaf is determined by a set of feature points at the leaf contour. The contour is extracted from images utilizing the curvature scale space corner detection algorithm. Auxin transport is described by an initial Auxin flow from a source to a sink that is gradually channelized into cells with large amounts of highly polarized transporters. The proposed model simulates leaf forms ranging from simple shapes to lobed leaves. The third level of venation system is generated using centroidal Voronoi tessellations and minimum spanning trees, whereas the size of each cell within the Voronoi-diagram is related to the involved quantity of Auxin.