Reaction–diffusion theoryThe paper 'The chemical basis of morphogenesis' [Phil. Trans. R. Soc. Lond.B237, 37鈥 72 (1952)] by Alan Turing remains hugely influential in the development of mathematical biology as a field of research and was his only published work in the area. In this ...
From 1950 Turing worked on a new mathematical theory of morphogenesis, based on showing the consequences of non-linear equations for chemical reaction and diffusion (Turing 1952). He was a pioneer in using a computer for such work. Some writers have referred to this theory as founding Artificial...
and Turing seized on the concept of the machine.Turing’s solution lay in defining what was soon to be named the Turing machine. With this he defined the concept of ‘the mechanical’ in terms of simple atomic operations. The Turing machine formalism was modelled on the tele...
Temporal Self-Organization: A Reaction-Diffusion Framework for Spatiotemporal Memories Inspired by the pioneering work of Alan Turing, who used reaction-diffusion equations to explain spatial pattern formation, we develop an analogous ... P Gowgi,SG Srinivasa - 《IEEE Transactions on Neural Networks ...
Like all the best scientific ideas, Turing’s theory was elegant and simple: any repeating natural pattern could be created by the interaction of two things — molecules, cells, whatever — with particular characteristics. Through a mathematical principle he called ‘reaction–diffusion’, these two...
"reaction-diffusion" systems , diffusion clashes with individual chemical reactions leading to the apparent paradox of the overall system getting more complicated over time. the same process that might lead to spots and patterns on animals also works on the molecular level, and some consider turing...
Can the French flag and reaction–diffusion models explain flower patterning? Celebrating the 50th anniversary of the French flag model Sixty-seven years ago, Alan Turing introduced the idea of patterns initiating de novo from a reaction鈥揹iffusion network. Together these models have been... VBV...
However, in biology he was a pioneer in suggesting how shapes like limbs and wings could develop from an embryo using morphogens – small molecules that diffuse and react with other molecules in reaction-diffusion networks. Although the details were wrong because almost nothing was known at the ...