Watching the Daisies Grow: Turing and Fibonacci Phyllotaxis

Abstract

Turing’s seminal 1952 paper on morphogenesis is widely known. Less well known is that he spent the last few years of his life further developing his morphogenetic theory and using the new computer to generate solutions to reaction-diffusion systems. Among other things, he claimed at one point to be able to explain the phenomenon of “Fibonacci phyllotaxis”: the appearance of Fibonacci numbers in the structures of plants. He never published this work, but did leave a nearly complete manuscript on morphogenesis and lattice phyllotaxis, together with more fragmentary notes on Fibonacci phyllotaxis. I discuss evidence that he developed a number of key ideas close to modern thinking, and tantalising hints that he came very close to a mathematical explanation of how the “daisy grows” into these patterns.