Mathematical Phyllotaxis

Jonathan Swinton has worked for thirty years as a mathematical biologist in university plant science and zoology departments and in the pharmaceutical industry. He  is a long erstwhile Fellow of King’s College Cambridge and nearly as erstwhile Visiting Professor in Systems Biology in the University of Oxford. Mathematical Phyllotaxis is based on invited graduate lectures that Jonathan gave in the University of Cambridge from 2019 onwards. His social and intellectual group biography Alan Turing’s Manchester  was published in 2018. Shining Molly, his new biography of the psychologist Molly Harrower, has been accepted for publication by the University of Akron Press in 2025.

• Motivation and outline.- Fibonacci numbers, the golden ratio, and co-prime integers.- Co-primality, continued fractions, and Möbius maps.- The geometry of cylindrical lattices.- Classifying cylindrical lattices.- Transformed Lattices.- Developmental biology of the plant.- Statisical phyllotaxis.- Placement models.- Stacked-disk models.- Some future directions.