- Snapshots of modern mathematics
- Pierre de Fermat and Andrew Wiles in Czech Republic stamps
- Stefan Banach (March 30, 1892 – August 8, 1945)
- Guessing the Numbers
- What is mathematics for Ehrhard Behrends
- What is mathematics for Krzysztof Ciesielski
- The Three Ducks Trick
- What is mathematics for Franka Brueckler

# Turing, Fibonacci and the sunflowers

*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: 10.1007/978-3-662-05642-4_20 (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

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: 10.1007/978-3-662-05642-4_20 (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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