Stable advection‐reaction‐diffusion with arbitrary anisotropy

Turing first theorized that many biological patterns arise through the processes of reaction and diffusion. Subsequently, reaction‐diffusion systems have been studied in many fields, including computer graphics. We first show that for visual simulation purposes, reaction‐diffusion equations can be made unconditionally stable using a variety of straightforward methods. Second, we propose an anisotropy embedding that significantly expands the space of possible patterns that can be generated. Third, we show that by adding an advection term, the simulation can be coupled to a fluid simulation to produce visually appealing flows. Fourth, we couple fast marching methods to our anisotropy embedding to create a painting interface to the simulation. Unconditional stability is maintained throughout, and our system runs at interactive rates. Finally, we show that on the Cell processor, it is possible to implement reaction‐diffusion on top of an existing fluid solver with no significant performance impact. Copyright © 2007 John Wiley & Sons, Ltd.