Turing, Fibonacci and the sunflowers

Today is the american Fibonacci's day, so it could be a good day to write something about one of the last work by Alan Turing.

One of a number of problems [Alan Turing] was trying to solve was the appearence of Fibonacci numbers in the structure of plants.⁽¹⁾

The problem was knwon as the Fibonacci phyllotaxis, and we can state it in this way:

the spiral shapes on the heads of sunflowers seemed to follow the Fibonacci sequence, prompting [Turing's] proposal that by studying sunflowers we might better understand how plants grow

Turing wrote his interest in a letter to the zoologist JZ Young: About the point (iii) Turing wrote in another letter:

Our new machine is to start arriving on Monday. I am hoping to do something about 'chemical embyology'. In particular I think I can account for the appearence of Fibonacci numbers in connection with fir-cones.⁽¹⁾

The last year Jonathan Swinton, during the Manchester Science Festival in October, announced the results of the great experiment about the Turing's sunflower:

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An happy Fibonacci's day!

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(1) Swinton J. (2004). Watching the Daisies Grow: Turing and Fibonacci Phyllotaxis, Alan Turing: Life and Legacy of a Great Thinker, 477-498. DOI: 10.1007/978-3-662-05642-4_20 (pdf)