Alan Turing's chemical theory of phyllotaxis

Abstract

Alan Turing's seminal 1952 work on morphogenesis \cite{Turing} is widely known and recognised in the field of mathematical biology. Less known is his work on the problem of phyllotaxis, which was never published at his time but is included in Turing's collected works \cite{Saunders}. It consists on three parts: the first is a detailed mathematical description of the arrangements of leaves on the stem of plants; the second is an application of the reaction-diffusion equation to the problem, and the third part is a solution of these equation for the case of spherical symmetry. It is the purpose of this work to present Turing's results contained in the second part in a comprehensive and detailed way. This is motivated by the fact that these researches have remained obscure and ill-understood. In particular, we focus on the morphogen equations for an assembly of cells since this discrete case may be useful in many circumstances where the continuum limit is not adequate or applicable.