Math may be hard, but it sure is handy – even in the world of fairies. Looking for an explanation for the so-called fairy circles – mysterious circles of grass found in Namibia and Western Australia -- researchers turned to one of the greatest mathematical minds of modern times, and Alan Turing, speaking from beyond the grave, gave them the answer. Was there any secret Turing couldn’t decode?
“Turing’s concept was that in certain systems, due to random disturbances and a “reaction-diffusion” mechanism, interaction between just two diffusible substances was enough to allow strongly patterned structures to spontaneously emerge.”
What? Fortunately, most of the press release on a new paper published in the Journal of Ecology is written at a more understandable level. In 1952 (he died in 1954 at the age of 41), Turing published a paper on mathematical biology considered by many to be his masterpiece: "The Chemical Basis of Morphogenesis." Morphogenesis is the development of patterns and shapes in biological organisms and Turing used a set of partial differential equations to model catalytic chemical reactions that could create regular patterns in nature. While Turing couldn’t take it any further, many other scientists did, using his work to explain spots and stripes on animals and the growth patterns of feathers and hair follicles. While it was thought that Turing’s pattern theory might help explain the patterns fairy circles formed, no one had accomplished it … until now.
“The data show that the unique gap pattern of the Australian fairy circles, which occur only in a small area east of the town of Newman, emerges from ecohydrological biomass-water feedbacks from the grasses. In fact, the fairy circles – with their large diameters of 4m, clay crusts from weathering and resultant water run-off – are a critical extra source of water for the dryland vegetation. Clumps of grasses increased shading and water infiltration around the nearby roots.”
An international research team led by Göttingen University scientists converged on Newman with a tool that had never been used to study these fairy circles before – one that Turing could only have imagined … drones. Using a drone equipped with a multispectral camera, the researchers mapped Triodia grasses over time in five one-hectare plots and classified them according to how well they grew. (Photos here.) They found that the areas doing well did so by cooperating to ring a small section in order to capture and hold moisture that normally would have run off. The mounded circle of grass also provided shade for new seedlings. However, the best part was that the photos showed that the grasses knew exactly how big to build the circles for irrigation and growth efficiency, and all of them did it the same way.
“The intriguing thing is that the grasses are actively engineering their own environment by forming symmetrically spaced gap patterns. The vegetation benefits from the additional runoff water provided by the large fairy circles, and so keeps the arid ecosystem functional even in very harsh, dry conditions.”
The circles of grass reacted with each other, just as Turing’s pattern theory had predicted. No fairies, gods, spirits, dragons or any other mythical beings formerly used to explain the fairy circles were needed – just the mathematical mind of Alan Turing.
Still think math is hard? Turing had an answer for that too.
“Those who can imagine anything, can create the impossible.”
― Alan Turing