Turing, Fibonacci and the sunflowers

By on 23/06/2017
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Article previously published on Doc Madhattn. June 23, 2017: Happy Alan Turing 105th Birthday!


One of the last Alan Turing‘s work is about Fibonacci numbers in nature:

One of a number of problems [Alan Turing] was trying to solve was the appearence of Fibonacci numbers in the structure of plants.[1]Swinton J. (2004). Watching the Daisies Grow: Turing and Fibonacci Phyllotaxis, Alan Turing: Life and Legacy of a Great Thinker, 477-498. DOI: (pdf)

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

A sunflower with Fibonacci's spiral

A sunflower with Fibonacci’s spiral

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.[2]See note 1.

In 2012, Jonathan Swinton, during the Manchester Science Festival, announced the results of the great experiment about the Turing’s sunflower:

 

 

 

And finally results are published last year on Royal Society open science[3]Swinton, J., Ochu, E., & MSI Turing’s Sunflower Consortium. (2016). Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment. Royal Society open science, 3(5), 160091. doi:10.1098/rsos.160091: a great result for Alan Turing and citizen science!

References   [ + ]

1. Swinton J. (2004). Watching the Daisies Grow: Turing and Fibonacci Phyllotaxis, Alan Turing: Life and Legacy of a Great Thinker, 477-498. DOI: (pdf)
2. See note 1.
3. Swinton, J., Ochu, E., & MSI Turing’s Sunflower Consortium. (2016). Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment. Royal Society open science, 3(5), 160091. doi:10.1098/rsos.160091

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