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 meshworks 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 nondiffusible one that is responsible for the periodicity in time, and a second highly diffusible one that causes the pattern through space. The interactions described 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 traveling waves can emerge without pacemaker regions and that colliding waves can penetrate each other without annihilation. In other words, crossings of oblique lines can occur.