A theory about the occurrence of mathematical patterns in nature, developed by computer scientist and code-breaker Alan Turing before his death in 1954, has finally been proven.
Turing believed that the seeds in a sunflower head conform to the Fibonacci code, a sequence of numbers in which the next figure is the sum of the previous two: 0, 1, 1, 2, 3, 5, 8, 13 and so on.
And this weekend (October 28) in Manchester it was announced that Turing's theory was indeed correct, thanks to sunflower growers and counters around the world.
The finding was the result of a citizen science project called Turing's Sunflowers, the initial data from which has shown that 82 per cent of sunflowers recorded had a Fibonacci-type structure.
[Related story: Citizen scientists honour Alan Turing with sunflowers]
Professor Jonathan Swinton, one of the project's researchers, said that the study proved maths is an integral part of nature and could provide clues to help biologists understand plant health and development in the future.
"We have proved what Alan Turing observed when he looked at a few sunflowers in his own garden in Wilmslow," Professor Swinton, a computational biologist, said.
"Now we need to work together with biologists to understand the wider implications of different number patterns for plant growth."
Turing's Sunflowers, led by the Manchester Museum of Science & Industry and Manchester Science Festival, in association with The University of Manchester, aimed to complete Turing's final experiment in this the centenary year of his birth.
Turing's work on breaking the code of the German naval Enigma machines is credited with shortening World War II by several years. He's also widely considered to be the father of modern computing. But a 1952 charge of gross indecency for private homosexual activity, and an enforced course of chemical castration, led him to suicide.
To honour his legacy, thousands of people from around the world pledged to grow sunflowers and count the number of seed spirals running clockwise and anti-clockwise in the flower heads.
Data from 557 sunflowers received from seven countries to date has been analysed and 458 sunflowers showed Fibonacci sequence spiral counts.
Furthermore, in 26 flowers double Fibonacci sequences were observed, and in 33 flowers spiral counts revealed the Lucas series of numbers (similar to Fibonacci in that each figure in the series is the sum of the previous two figures, but it starts 2, 1, instead of 0, 1. Eg: 2, 1, 3, 4, 7, 11, 18, 29 and so on).
Turing's Sunflowers is the largest research attempt ever into the mathematical patterns in sunflowers, a study known as phyllotaxis.
Phyllotaxic observation goes back hundreds of years and has been investigated by a number of scientists, but never to the scale of the Turing's Sunflowers project.
The last recorded experiment to test Fibonacci phyllotaxis in sunflowers was in 1938 by the Dutch academic JC Schoute, who studied 319 samples.
The aim now is to publish the Turing's Sunflower results in a scientific paper and make the data available for further studies to explore the reasons why these different number patterns occur in nature.
Dr Erinma Ochu, project manager of Turing's Sunflowers, said: "It's been brilliant to see sunflowers in bloom around the world and the power of citizens working together for this exciting mass experiment."
The project team were intrigued to find that some sunflowers showed beautiful examples of the spiral patterning but no Fibonacci numbers. Dr Ochu said it was these exceptions to the rule which were particularly interesting topics for future investigation.
"I'm delighted to have gathered a data set that can be used in the future by scientists to help understand why Fibonacci numbers occur in nature, and why they don't."