Biological action at a distance: Correlated pattern formation in adjacent tessellation domains without communication
Fig 2
The distribution of pattern correlations along common edges of tessellating triangles should be bimodal.
Colour images show typical patterns generated by a reaction-diffusion model with a large diffusivity term, using a colour map in which red and blue mark extreme high and low concentration values, and green marks zero concentration. A Solved within the boundary of an equilateral triangle, two basic patterns emerge, with extreme concentrations in one corner and along the opposite edge (left) or at two corners (right). Along the edges, three pattern types are apparent. Type 1 varies between the two extremes, type 2 varies between one extreme and zero, and type 3 does not vary. The probability of type i is given below as p(i). The table gives the probability that the absolute correlation between patterns sampled along two randomly chosen edges will be high (pa), medium (pb), or low (pc). As pc < pb < pa the distribution of correlations should be bimodal. B Patterns that emerge within the boundary of an isosceles triangle will be of type 1 or 3 only, changing the distribution of correlations across random edge pairs while retaining an overall bimodal distribution (pc < pa). However, if pairs of edges are restricted to those which may be adjacent in a tessellation then only pairs of type 1 and pairs of type 3 are possible, and pa = 1. Hence, in more general terms, the distribution of correlations between patterns measured along the edges of adjacent tessellation domains should be even more strongly bimodal.