Alan Turing was right: Sunflower spirals clearly show a mathematical sequence in most cases, according to early results from the largest research project of its kind carried out as part of a citizen science experiment led by MOSI (Museum of Science & Industry), Manchester, and announced today as part of the Manchester Science Festival (27 October – 4 November).
Initial findings of the Turing’s Sunflowers project, which celebrates the work of mathematician Alan Turing 100 years after his birth, show that 82 per cent of sunflowers had a Fibonacci-type structure, for example, where the number of spirals conformed to one of the numbers in the sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… (each number is the sum of the previous two). The study, which is the largest research attempt ever into the mathematical patterns in sunflowers, with unprecedented photographic evidence, proves that maths is an integral part of nature and could provide clues to help biologists understand plant health and development in the future.
Turing’s Sunflowers attracted involvement from people across the world who pledged thousands of sunflowers to the experiment. Citizen scientists, including many schoolchildren, were asked to provide measurements and data about their sunflowers, particularly the number of spirals running clockwise and anti-clockwise in the sunflower seedhead. Data from 557 sunflowers from seven countries has been analysed and 458 showed spiral counts as part of a Fibonacci sequence.
In a small number of cases 33 spiral counts were observed from the Lucas series of numbers (1, 3, 4, 7, 11…), and in 26 cases, double Fibonacci sequences (e.g. 21x2 or 34 x2) were noted. The project team were intrigued that some sunflowers showed beautiful examples of the spiral patterning but no Fibonacci numbers. It is these exceptions to the rule which are particularly interesting topics for future investigation. The aim is to publish the 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.
Professor Jonathan Swinton, a computational biologist, and one of the researchers, said: “I’m delighted that so many people have got involved in Turing’s Sunflowers and helped to provide this fascinating dataset, the results of which will be published shortly. It’s the most comprehensive information we have so far on Fibonacci numbers in sunflowers and we have proved what Alan Turing observed when he looked at a few sunflowers in his own garden in Wilmslow. Now we need to work together with biologists to understand the wider implications of different number patterns for plant growth.”
Dr Erinma Ochu, the Turing’s Sunflowers project manager said: “It’s been brilliant to see sunflowers in bloom around the world and just goes to show the power of citizens working together for this exciting mass experiment. Thousands of people contributed to Turing’s Sunflowers, and although we were hampered by bad weather and slugs in many cases I’m delighted to have gathered a dataset that can be used in the future by scientists to help understand why Fibonacci numbers occur in nature, and why they don’t.”
The results will be announced alongside a screening of the Turing’s Sunflower Diaries from footage shot by growers and directed by BBC Outreach staff volunteers. During the Festival, the Growers’ gallery of sunflower photographs from around the world will be on display at MOSI and Manchester Museum and a monologue performance about Alan Turing’s life will be shown at MOSI.
Mathematician and computer pioneer Alan Turing studied spirals in sunflowers for the occurrence of Fibonacci numbers (see notes), but he died in 1954, before the work was complete. The observation of Fibonacci phyllotaxis goes back hundreds of years and has been revisited by a number of others as well as Alan Turing. The last recorded experiment to test Fibonacci phyllotaxis in sunflowers was in 1938 by the Dutch academic JC Schoute, who studied 319 samples.
Turing wrote a seminal paper in 1951 on form in biology and went on to work on a specific theory to explain the appearance of Fibonacci numbers in plant structures, notably spirals on sunflower heads. His only surviving programs for the Manchester Mk1 computer were devoted to solving this problem. Yet the work was unfinished at his death and was little known about it until recently.
Turing’s Sunflowers is a MOSI initiative in association with Manchester Science Festival and supported by The University of Manchester and Manchester City Council. It was part of a series of events to celebrate the centenary of Manchester-based Alan Turing and his work.
For more information look up: www.turingsunflowers.com
For media enquiries please contact:
Sarah Roe, MOSI press and publicity officer on m: 07847 372647
Notes to editors
Turing’s Sunflowers partners include the BBC, CityCo, Corridor Manchester, Creative Tourist, Manchester Garden City, Manchester City Council, Manchester Museum, The National Trust and The University of Manchester.
Fibonacci numbers are the sequence 0,1,1,2,3,5,8,13,21,34,55, and so on, where each number is the sum of the two numbers before it.
About Manchester Science Festival
Manchester Science Festival is an annual nine-day, multi-venue festival that engages and inspires people with science, technology, engineering and maths; building their confidence in exploring and questioning science in the most creative ways possible. It is the North West’s premier cultural celebration of all things science. Last year there were 113,018 attendances at the Festival.
Manchester Science Festival is proudly produced by MOSI (Museum of Science & Industry, Manchester) in partnership with cultural, educational and business organisations across Greater Manchester. MOSI hosts around a third of the programme, with other events in cultural venues and unusual spaces in the city. There are also extensive programmes in Bolton and Salford.
MOSI is part of the Science Museum Group.