This is the second in a series of posts about the maths of Star Trek. Part I covered the probability of survival while wearing a red shirt.
Google Code, one of now approximately a million different websites which start with the word Google, is a sharing platform for developers to exchange open-source programs and nifty things they have made.
One such nifty thing is this Reaction-Diffusion package, based on our old friend Alan Turing’s famous equation. The reaction-diffusion equation, originally given in Turing’s 1952 paper The Chemical Basis of Morphogenesis, provides a model for how a mixture of chemicals, reacting with each other while moving under the action of diffusion, might result in the kind of patterns we see in animal print and elsewhere in nature.
BBC News are reporting that “thousands of sunflowers are to be planted in Greater Manchester to try to prove a theory put forward by a mathematics genius”.
The genius in question is Alan Turing who, in his work on mathematical biology, apparently theorised “that sunflower heads featured Fibonacci number sequences”. The BBC article explains that Turing:
wrote a paper in 1951 on form in biology and went on to work up a specific theory to explain why Fibonacci sequences appeared in plants.
However, he never had chance to test his theory…
The only surviving programs which he wrote for the Manchester Mk1, one of the world’s earliest modern computers, are devoted to proving his theories.
The BBC quotes Jonathan Swinton, who wrote a detailed article on Turing and Fibonacci Phyllotaxis in 2004, saying:
Since then other scientists believe that Turing’s explanation of why this happens in sunflowers is along the right lines but we need to test this out on a big dataset, so the more people who can grow sunflowers, the more robust the experiment.
The website for the project, Turing’s Sunflowers, part of the Manchester Science Festival, explains:
We need you to sow sunflower seeds in April and May, nurture the plants throughout the summer and when the sunflowers are fully grown we’ll be counting the number of spirals in the seed patterns in the sunflower heads. Don’t worry – expertise will be on hand to help count the seeds and you’ll be able to post your ‘spiral counts’ online.
The results will be announced during the Manchester Science Festival 2012 (27 Oct – 4 Nov), alongside a host of cultural events connected to Turing’s life and legacy, at MOSI, Manchester Museum and other cultural spaces.
Source: BBC News – Greater Manchester sunflowers to test Alan Turing theory.
Alan Turing’s research in the latter part of his life focused, among other things, on morphogensis – particularly of animal pattern formation. According to a King’s College London press release, Turing “put forward the idea that regular repeating patterns in biological systems are generated by a pair of morphogens that work together as an ‘activator’ and ‘inhibitor’”. Now researchers at Kings have provided experimental evidence to confirm this theory. This study:
not only demonstrates a mechanism which is likely to be widely relevant in vertebrate development, but also provides confidence that chemicals called morphogens, which control these patterns, can be used in regenerative medicine to differentiate stem cells into tissue.
The press release quotes Dr Jeremy Green from the Department of Craniofacial Development at King’s Dental Institute saying:
“Regularly spaced structures, from vertebrae and hair follicles to the stripes on a tiger or zebrafish, are a fundamental motif in biology. There are several theories about how patterns in nature are formed, but until now there was only circumstantial evidence for Turing’s mechanism. Our study provides the first experimental identification of an activator-inhibitor system at work in the generation of stripes – in this case, in the ridges of the mouth palate.
“Although important in feeling and tasting food, ridges in the mouth are not of great medical significance. However, they have proven extremely valuable here in validating an old theory of the activator-inhibitor model first put forward by Alan Turing in the 50s.
“Not only does this show us how patterns such as stripes are formed, but it provides confidence that these morphogens (chemicals) can be used in future regenerative medicine to regenerate structure and pattern when differentiating stem cells into other tissues.”
Source: Scientists prove Turing’s tiger stripe theory.