In this chapter, especially in Section 5.2.2, I give a fair amount of detail on how one goes about a computational project to explore the ability of reaction–diffusion mechanisms to generate a sequence of dichotomous branchings as they are observed in a rather complex morphogenesis of a single cell. Several generalities should be borne in mind by the reader: first, we are not merely pursuing the objective of the animator and many practitioners of computer graphics to draw a good moving picture of something no matter how we do it. Our objective is that of the developmental biologist: to draw the plant and its development the way the plant does it.
Second, many readers, including experimental biologists, may have no clear concept of what it takes to do the theoretical side of a project in developmental biology. The message here is that, in proper pursuit of the scientific method, experiment and theory are about equally time-consuming. I hope that Section 5.2.2 illustrates how the theoretical work requires groups with graduate students and postdoctoral fellows fully devoted to it, just as biological experimentation does.
Third, as one pursues such a theoretical project, one gradually begins to realize more and more that negative-looking features of the postulated mechanisms are essential to getting the right development of shapes. For plants with many small and separate growing regions, how their boundaries are established and how they manage to move to keep the active regions small is often more important than what is going on inside the active regions.