Parallel simulation of accretive growth and form in three dimensions

A geometric model for diffusion-limited radiate accretive growth is used to simulate the emergence of growth and form of a certain class of organisms and crystals. In the model, layered structures are generated by the construction of new layers on top of the previous ones, the local growth velocities are determined by the local nutrient concentration gradients. The simulation of nutrient-limited growth in three dimensions (3D) is computationally very expensive. This paper presents a methodology to formulate the geometrical problem in terms of a 3D Laplace solver and maps this solver on a parallel platform. The aim of this paper is to demonstrate that this hybrid method is capable of simulating two typical properties of radiate accretive growth: (1) the indeterminateness of the growth process; and (2) the strong impact of the physical environment on the growth process.