Physically-based simulation of plant leaf growth

A mathematical model is presented to simulate the growth of a plant leaf. The tissue in the leaf has been regarded as a viscous, incompressible fluid whose 2D expansion comes from the non-zero specific growth rate in area. The resulting system of equations are composed of the modified Navier-Stokes equations. The level set method is used to capture the expanding leaf front. Numerical simulations indicate that different portions of the leaf expand at different rates, which is consistent with the biological observations in the growth of a plant leaf. Numerical results for the case of the Xanthium leaf growth are also presented. A standard ray tracing technique is applied to produce an animation simulating the leaf growth process of three days. The key results with their physical and practical implications are discussed. Copyright # 2004 John Wiley & Sons, Ltd.