Geometrical Constraints on the Development of a Diatom

In a plane hexagonal array of pores such as occurs in Thalassiosira oestrupii and other related species of marine diatom, the presence of a single, exceptional pore near the center of the array can cause the distortion in the pattern in such a way that the pores tend to diminish in diameter D with increasing distance R from the center. By a simple mathematical argument it is shown that for large values of R/D the pore diameter D varies as R−1/6. This decrease in pore diameter with distance may have some developmental consequences. The law is generalized to other types of pattern. The second type of constraint, related to the presence of outer boundaries, is also discussed.