Abstract
Two-dimensional arrays of pores on cell walls of Micrasterias rotata and Cosmarium botrytis show a high degree of order. We review various measures of order and choose to analyze the data in terms of Clark & Evans' (1954) R parameter. The experimental R values are high, but not high enough to demand the precise ordering abilities of a morphogen wave mechanism. Following Claxton (1964), we show that the patterns are compatible with random and continuous nucleation of pore initials, each of which inactivates a circular inhibitory field around it against further nucleation. We discuss several versions of a model in which inhibition is produced by depletion of a substance, needed both for growth and for nucleation, below a critical concentration for the latter. This critical behaviour is probably analogous to the critical micelle concentration in detergent solutions, not the critical supersaturation of classical nucleation theory in phase transitions. The growing nuclei must rapidly reach constant radius. The size of the inhibitory fields requires diffusion to be in two (not three) dimensions.
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