Crossings, meshwork of oblique lines and staggered dots: the combined action of two antagonists

Many shells display simple periodic patterns that cannot be accounted for with the elementary mechanisms described so far. Patterns of staggered dots and mesh-works belong in this class (Figure 5.1). These patterns are characterized by a periodicity along the time coordinate as well as along the space coordinate. This suggests that two antagonists are involved: a non-diffusible one that is responsible for the periodicity in time, and a second highly diffusible one that causes the pattern through space. The interactions described by the equations in this chapter are possible extensions of the activator-substrate and the activator-inhibitor model (see boxes). An important property of such mechanisms is that travelling waves can penetrate each other without annihilation. In other words, crossings of oblique lines can occur.