Historical meeting again

Past chapters in this book very often mention Bravais and Bravais who successfully worked on the problem of phyllotaxis in the 1830s (Bravais– Bravais theorem, lattice, formula, etc.). One of the reasons for this success might be that these brothers were a botanist and a crystallographer. In those times living organisms were generally perceived as living crystals. That the crystallographic paradigm was shortly abandoned after the Bravais brothers may explain the relatively poor development of the subject of phyllotaxis in the second half of the nineteenth century. Van Iterson (1907) introduced geometrical methods of analysis of phyllotactic patterns based on symmetry theories of crystal structures. His work received very little attention and was revived to some extent in the second part of the century by botanists and mathematicians dealing with phyllotaxis in terms of contact circles on cylinders. The fact that crystallographers have rejoined the effort very recently might be an unconscious collective historical recognition that the discipline was from its very beginning under a good omen, and that the intuition of the initiators of the cylindrical treatment of phyllotaxis put the subject on the right track.

For crystallographers all aspects of the challenge of phyllotaxis are excluded except the geometrical aspect, and phyllotaxis is identified with the study of spiral lattices.