Parts I, II and III of the monograph can be summarized in the following way: (1) what the patterns are (description), (2) what they are for (functionality), and (3) what they have been (origins). Part III pledges a broader approach to phyllotaxis than students are generally accustomed to. The object of the monograph was to present a universal theory of phyllotaxis. Despite its flaws in the general setting of morphogenesis, it is the first such theory.

Part III introduced two important phenomena: the phenomenon of emergence and the phenomenon of homology. It has been recognized that the whole system called a primordial pattern has properties that are not exhibited by the constituting units, the primordia. Emergence means that the whole is more than the sum of its parts. A famous example is sodium chloride (NaCl), which has (emergent) properties quite different from those of sodium and chlorine taken separately. Another example is an impressionistic painting, which is more than the sum of its dots of paint. Of course, as the systems become increasingly complex the results of emergence become more and more striking. Sattler (1986) emphasized that some biologists continue to argue that the most important levels of organization are the cellular and molecular. He discusses the inadequacy of this view in the context of the phenomenon of emergence [the plant forms cells, not cells the plant, as Barlow (1982) points out]. Although a knowledge of the elementary units is a prerequisite, it is not sufficient for understanding phyllotaxis.