however, this was never to be. although the continuous growth model could have very easily been extended to incorporate a model for photosynthate creation and transport, I was only doing a one-year masters degree. and I decided to investigate another area in depth - dynamic simulation of trees.
the equations for elastic deformation can be used to determine how an idealised cylindrical section of wood responds when a force is applied to it. this lets us build a system of differential equations which can be numerically integrated over time. propagate these forces up and down the tree, and voila! your tree can droop under gravity and blow in the wind.
those of you with any experience at doing this sort of thing are undoubtedly wincing already. as I know now, this is the classic example of a 'stiff system'. the trunk of a 200-meter redwood is in almost perfect equilibrium, and it would take an unimaginable force to bend it a single degree. yet the leaves swaying on its branches are floppy and sway about on a very small timescale. this is the kind of numerical problem that can explode at the slightest provocation. throw in the fact that there's really no way to represent 'bending' in a smooth domain without any singularities, and you're in for a wild ride.
recently, there have been advances in numerical integration that allow this kind of problem to be solved. baraff and witkin's siggraph 98 paper describes an implicit formulation developed for cloth modelling. this turns around the stiff problem of a large spring mass and uses sparse-matrix techniques to run screamingly fast and generate amazing results.