The problem of the origins of phyllotactic patterns can be dealt with at many different levels. In the study of higher plants Bolle's theory represents a preliminary level, and Zimmermann's theory a second level which proposes to go back to the ancestral land plants. Church's perspective on phyllotaxis proposes to go back to the sea to understand the primary meaning and function of the patterns found in higher plants. The first three levels have been considered in Chapters 3 and 8.

We have seen in Part I that phyllotactic patterns are branched structures and hierarchies. They were present at the beginning of the evolution of land plants, and are found in brown algae as well. Branching is one of the most fundamental growth processes, present in the structure of the sunflower, one of the most striking example of phyllotaxis (see Section 3.3) and of floral evolution. But these branched structures are also seen in minerals and animals, so that it is not surprising to see phyllotaxis–like patterns in other areas of nature, as Part III will show.

Chapter 10 presents my application of phyllotactic methods and of the theorem of Chapter 2 to protein crystallography, and makes predictions of what should be an exact representation of patterns of amino acid residues in polypeptide chains. The chapter examines the work of contemporary botanists and crystallographers who understood the relevance of the crystallographic paradigm in phyllotaxis.