Much of the geometrical complexity of animals and plants arises by the repetition of similar structures, often in a pattern which is constant for a species. In an earlier paper (Maynard Smith, 1960) some of the mechanisms whereby a constant number of structures in a linear series might arise were discussed. In this paper an attempt is made to extend the argument to cases where such structures are arranged in two-dimensional patterns on a surface, using the arrangement of bristles in Drosophila as illustrative material.
The bristles of Drosophila fall into two main classes, the microchaetes and the macrochaetes. A bristle of either type, together with its associated sensory nervecell, arises by the division of a single hypodermal cell. The macrochaetes are larger, and constant in number and position in a species, and in most cases throughout the family Drosophilidae.
Asymptotic constructions and invariants of graded linear series
