Editing Alan Turing (section)

===Pattern formation and mathematical biology===
When Turing was 39 years old in 1951, he turned to [[Mathematical and theoretical biology|mathematical biology]], finally publishing his masterpiece "[[The Chemical Basis of Morphogenesis]]" in January 1952. He was interested in [[morphogenesis]], the development of patterns and shapes in biological organisms. He suggested that a system of chemicals reacting with each other and diffusing across space, termed a [[reaction–diffusion system]], could account for "the main phenomena of morphogenesis".<ref name=chemical>{{cite Q|Q769913 }}</ref> He used systems of [[partial differential equations]] to model catalytic chemical reactions. For example, if a catalyst A is required for a certain chemical reaction to take place, and if the reaction produced more of the catalyst A, then we say that the reaction is [[autocatalytic]], and there is positive feedback that can be modelled by nonlinear differential equations. Turing discovered that patterns could be created if the chemical reaction not only produced catalyst A, but also produced an inhibitor B that slowed down the production of A. If A and B then diffused through the container at different rates, then you could have some regions where A dominated and some where B did. To calculate the extent of this, Turing would have needed a powerful computer, but these were not so freely available in 1951, so he had to use linear approximations to solve the equations by hand. These calculations gave the right qualitative results, and produced, for example, a uniform mixture that oddly enough had regularly spaced fixed red spots. The Russian biochemist [[Boris Pavlovich Belousov|Boris Belousov]] had performed experiments with similar results, but could not get his papers published because of the contemporary prejudice that any such thing violated the [[second law of thermodynamics]]. Belousov was not aware of Turing's paper in the ''[[Philosophical Transactions of the Royal Society]]''.<ref>{{Cite book |first=John |last=Gribbin |title=Deep Simplicity |page=126 |publisher=Random House |year=2004}}</ref>

Although published before the structure and role of [[DNA]] was understood, Turing's work on morphogenesis remains relevant today and is considered a seminal piece of work in mathematical biology.<ref>{{cite web|url=http://www.swintons.net/deodands/archives/000087.html |title=Turing's Last, Lost work |access-date=28 November 2011 |url-status=dead |archive-url=https://web.archive.org/web/20030823032620/http://www.swintons.net/deodands/archives/000087.html |archive-date=23 August 2003 }}</ref> One of the early applications of Turing's paper was the work by James Murray explaining spots and stripes on the fur of cats, large and small.<ref>{{cite journal | last=Murray | first=James D. | title=How the Leopard Gets Its Spots | journal=Scientific American  | volume=258 | issue=3 | date=March 1988 | jstor=24989019 | pages=80–87 | doi=10.1038/scientificamerican0388-80 | bibcode=1988SciAm.258c..80M }}</ref><ref>{{Cite book |first=James D. |last=Murray |title=Mathematical Biology I |year=2007 |chapter=Chapter 6 |publisher=Springer Verlag}}</ref><ref>{{Cite book |first=John |last=Gribbin |title=Deep Simplicity |page=134 |publisher=Random House |year=2004}}</ref> Further research in the area suggests that Turing's work can partially explain the growth of "feathers, hair follicles, the branching pattern of lungs, and even the left-right asymmetry that puts the heart on the left side of the chest".<ref>{{cite journal|doi=10.1126/science.338.6113.1406|pmid=23239707|title=Turing Pattern Fingered for Digit Formation|journal=Science|volume=338|issue=6113|pages=1406|year=2012|last1=Vogel|first1=G.|bibcode=2012Sci...338.1406V}}</ref> In 2012, Sheth, et al. found that in mice, removal of [[Hox genes]] causes an increase in the number of digits without an increase in the overall size of the limb, suggesting that Hox genes control digit formation by tuning the wavelength of a Turing-type mechanism.<ref>{{Cite journal |last1 = Sheth |first1 = R. |last2 = Marcon |first2 = L. |last3 = Bastida |first3 = M.F. |last4 = Junco |first4 = M. |last5 = Quintana |first5 = L. |last6 = Dahn |first6 = R. |last7 = Kmita |first7 = M. |last8 = Sharpe |first8 = J. |last9 = Ros |first9 = M.A. |doi = 10.1126/science.1226804 |title = Hox Genes Regulate Digit Patterning by Controlling the Wavelength of a Turing-Type Mechanism |journal = Science |volume = 338 |issue = 6113 |pages = 1476–1480 |year = 2012 |pmid = 23239739 |pmc = 4486416 |bibcode = 2012Sci...338.1476S }}</ref> Later papers were not available until ''Collected Works of A.&nbsp;M.&nbsp;Turing'' was published in 1992.<ref>{{cite web|title=The Alan Turing Bibliography|url=http://www.turing.org.uk/sources/biblio3.html|page=morphogenesis|publisher=turing.org.uk|access-date=27 July 2015|author=Andrew Hodges|archive-url=https://web.archive.org/web/20150905180420/http://www.turing.org.uk/sources/biblio3.html|archive-date=5 September 2015|url-status=live}}</ref>

A study conducted in 2023 confirmed Turing's mathematical model hypothesis. Presented by the [[American Physical Society]], the experiment involved growing [[chia seed]]s in even layers within trays, later adjusting the available moisture. Researchers experimentally tweaked the factors which appear in the Turing equations, and, as a result, patterns resembling those seen in natural environments emerged. This is believed to be the first time that experiments with living vegetation have verified Turing's mathematical insight.<ref>{{cite news|url=https://www.sciencenews.org/article/seeds-alan-turing-patterns-nature-math|author=James R. Riordon|date=26 March 2023|title=Chia seedlings verify Alan Turing's ideas about patterns in nature|work=Science News|access-date=26 August 2024|archive-date=2 July 2024|archive-url=https://web.archive.org/web/20240702160511/https://www.sciencenews.org/article/seeds-alan-turing-patterns-nature-math|url-status=live}}</ref><ref>{{cite news|url=https://meetings.aps.org/Meeting/MAR23/Session/F46.3|author=Brendan D'Aquino|date=7 March 2023|title=Abstract: F46.00003 : Studying Turing patterns in vegetation|work=American Physical Society|access-date=26 August 2024|archive-date=2 July 2024|archive-url=https://web.archive.org/web/20240702162242/https://meetings.aps.org/Meeting/MAR23/Session/F46.3|url-status=live}}</ref>