**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Turing pattern

Summary

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. The pattern arises due to Turing instability which in turn arises due to the interplay between differential diffusion (i.e., different values of diffusion coefficients) of chemical species and chemical reaction. The instability mechanism is unforeseen because purely diffusion process is anticipated to have a stabilizing influence on the system.
In his paper, Turing examined the behaviour of a system in which two diffusible substances interact with each other, and found that such a system is able to generate a spatially periodic pattern even from a random or almost uniform initial condition. Prior to the discovery of this instability mechanism arising due to unequal diffusion coefficients of the two substances, diffusional effects were always presumed to have stabilizing influences on the system.
Turing hypothesized that the resulting wavelike patterns are the chemical basis of morphogenesis. Turing patterning is often found in combination with other patterns: vertebrate limb development is one of the many phenotypes exhibiting Turing patterning overlapped with a complementary pattern (in this case a French flag model).
Before Turing, Yakov Zeldovich in 1944 discovered this instability mechanism in connection with the cellular structures observed in lean hydrogen flames. Zeldovich explained the cellular structure as a consequence of hydrogen's diffusion coefficient being larger than the thermal diffusion coefficient. In combustion literature, Turing instability is referred to as diffusive–thermal instability.
The original theory, a reaction–diffusion theory of morphogenesis, has served as an important model in theoretical biology. Reaction–diffusion systems have attracted much interest as a prototype model for pattern formation.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related courses (4)

Related publications (186)

Related people (31)

Related concepts (8)

Related lectures (31)

Related units (7)

Ontological neighbourhood

BIO-244: Physics of the cell

Living organisms evolve in a physical world: their cells respond to mechanics, electricity and light. In this course, we will describe the behavior and function of cells using physical principles.

MATH-642: Artificial Life

We will give an overview of the field of Artificial Life (Alife). We study questions such as emergence of complexity, self-reproduction, evolution, both through concrete models and through mathematica

ChE-402: Diffusion and mass transfer

This course aims to provide an in-depth understanding of diffusion and mass transfer, an essential tool for the
chemical engineers.

"The Chemical Basis of Morphogenesis" is an article that the English mathematician Alan Turing wrote in 1952. It describes how patterns in nature, such as stripes and spirals, can arise naturally from a homogeneous, uniform state. The theory, which can be called a reaction–diffusion theory of morphogenesis, has become a basic model in theoretical biology. Such patterns have come to be known as Turing patterns. For example, it has been postulated that the protein VEGFC can form Turing patterns to govern the formation of lymphatic vessels in the zebrafish embryo.

Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time.

Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side.

The Industrial Revolution and Machinery Introduction

Explores the Industrial Revolution, its concepts, impacts, and societal perspectives, emphasizing historical interpretations and growth patterns.

Inkjet-based Patterning and Gravure Printing

Delves into inkjet-based patterning and gravure printing processes, analyzing pattern formation, drying effects, and transfer mechanisms.

Cell Patterning and Signalling Pathways

Explores cell patterning, signalling pathways, and genetic mutations in biological development.

Surface stress drives long-range elastocapillary interactions at the surface of compliant solids, where it has been observed to mediate interparticle interactions and to alter the transport of liquid drops. We show that such an elastocapillary interaction ...

2023Mutations to gene regulatory networks can be maladaptive or a source of evolutionary novelty. Epistasis con-founds our understanding of how mutations affect the expression patterns of gene regulatory networks, a chal-lenge exacerbated by the dependence of ...

Matthias Lütolf, Alexandre Gauthier Aurèle Mayran, Stefano Davide Vianello, Raphaël Ortiz

Gastruloids are 3D structures generated from pluripotent stem cells recapitulating fundamental principles of embryonic pattern formation. Using single-cell genomic analysis, we provide a resource mapping cell states and types during gastruloid development ...