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   How did Turing explain the development of patterns?

   • To explain the development of patterns, Turing proposed the addition of instability to a linear system of molecular movement by introducing diffusion of morphogens at specific time points.

   Turing patterns, 70 years later | Nature Computational Science

   www.nature.com/articles/s43588-022-00306-0

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   What is a Turing pattern?

   • In theory, a Turing pattern can be a perfectly ordered lattice of spots or array of stripes, but in practice, random defects interrupt this perfection, producing a quasi-regular pattern. Straight away it’s obvious why Turing’s theory looked like a good candidate for explaining the zebra’s stripes and the leopard’s spots.

   Turing patterns | Feature | Chemistry World

   www.chemistryworld.com/features/turing-patterns/4991.article

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   Can Turing patterns explain things in nature?

   • Lots of scientists are using Turing patterns to help explain things in nature. James D Murray used Turing’s mathematics to recreate animal coat patterns. Murray showed that Turing patterns explain why we see animals with spotted bodies and stripy legs and tails! Murray showed that as tails and legs get thinner, spots turn to stripes.

   Turing Pattern Project - Turing patterns - University of Sheffield

   turing-pattern-project.sites.sheffield.ac.uk/turing-patterns

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   What is Alan Turing theory?

   • Nearly seventy years ago Alan Turing, a pioneer of Computer Science, developed a theory to explain how certain patterns in nature could arise spontaneously from simple chemical systems. This idea was a significant departure from much of his previous work on the theory of computation, and used very different kinds of mathematics.

   A Modern View on Turing’s Theory of Pattern Formation

   royalsociety.org/blog/2021/11/turing-theory-pattern-formation/

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   What is Turing best known for?

   • Turing is best known for his work on computing, and it was his computational approach to mathematics that led to the reaction–diffusion theory. Before computing became widespread, linear differential equations were used to describe patterns — but they can only explain how a pattern can be amplified, not generated.

   70 years of Turing patterns | Nature Reviews Physics

   www.nature.com/articles/s42254-022-00486-8

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   What is Turing's theory of chemical pattern formation?

   • Turing’s theory of chemical pattern formation, now vindicated experimentally, looks like the best candidate for explaining a variety of puzzles in biological development, from the spontaneous differentiation of some tissues to the formation of pigmented markings and the patterns of leaves on plant stems.

   Turing patterns | Feature | Chemistry World

   www.chemistryworld.com/features/turing-patterns/4991.article

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3. en.wikipedia.org › wiki › Turing_patternTuring pattern - Wikipedia

   en.wikipedia.org › wiki › Turing_pattern

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   The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state.

4. www.nature.com › articles › s43588/022/00306-0Turing patterns, 70 years later | Nature Computational Science

   www.nature.com › articles › s43588/022/00306-0

   Aug 14, 2022 · To explain the development of patterns, Turing proposed the addition of instability to a linear system of molecular movement by introducing diffusion of morphogens at specific time...

5. royalsociety.org › turing-theory-pattern-formationA Modern View on Turing’s Theory of Pattern Formation

   royalsociety.org › turing-theory-pattern-formation

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   Nov 8, 2021 · Nearly seventy years ago Alan Turing, a pioneer of Computer Science, developed a theory to explain how certain patterns in nature could arise spontaneously from simple chemical systems. This idea was a significant departure from much of his previous work on the theory of computation, and used very different kinds of mathematics.

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     Can One Mathematical Model Explain All Patterns In Nature?

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     New theory deepens understanding of Turing patterns

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     Exploring Turing Patterns at Atomic Levels

     16 Nov 2022

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7. www.chemistryworld.com › features › turing-patternsTuring patterns | Feature | Chemistry World

   www.chemistryworld.com › features › turing-patterns

   Turing proposed that an embryo becomes patterned into regions with different anatomical fates by chemical substances called morphogens (literally ‘shape-formers’), which diffuse through ...

8. turing-pattern-project.sites.sheffield.ac.ukTuring Pattern Project - Turing patterns

   turing-pattern-project.sites.sheffield.ac.uk

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   Have you ever wondered why the hairs on our arms grow in a spotted pattern or why our fingerprints have that striped pattern? Alan Turing’s mathematics tells us how these patterns can appear. Lots of scientists are using Turing patterns to help explain things in nature.

9. www.nature.com › articles › s42254/022/00486-870 years of Turing patterns | Nature Reviews Physics

   www.nature.com › articles › s42254/022/00486-8

   Jun 22, 2022 · In the 50 years since, Turing patterns have been found in many biological systems, including leopard spots, ladybird shells and bird feathers.

10. theconversation.com › alan-turing-how-the-worldsAlan Turing: how the world’s most famous codebreaker unlocked ...

    theconversation.com › alan-turing-how-the-worlds

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    Jun 28, 2019 · Aided by modern computers, scientists have shown that Turing’s equations can be used to mimic countless two-dimensional patterns seen across the natural world, from fingerprints and the...