"The Chemical Basis of Morphogenesis" is an article that the English mathematician

Alan Turing Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical co ...

wrote in 1952. It describes how

patterns in nature 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, ...

, 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 Morphogenesis (from the Greek ''morphê'' shape and ''genesis'' creation, literally "the generation of form") is the biological process that causes a cell, tissue or organism to develop its shape. It is one of three fundamental aspects of deve ...

, has become a basic model in

theoretical biology 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 a ...

. 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 The zebrafish (''Danio rerio'') is a freshwater fish belonging to the minnow family (Cyprinidae) of the order Cypriniformes. Native to South Asia, it is a popular aquarium fish, frequently sold under the trade name zebra danio (and thus often ca ...

embryo.

Reaction–diffusion systems

Reaction–diffusion systems have attracted much interest as a prototype model for

pattern formation The science of pattern formation deals with the visible, ( statistically) orderly outcomes of self-organization and the common principles behind similar patterns in nature. In developmental biology, pattern formation refers to the generation of ...

. Patterns such as fronts, spirals, targets, hexagons, stripes and dissipative solitons are found in various types of reaction-diffusion systems in spite of large discrepancies e.g. in the local reaction terms. Such patterns have been dubbed " Turing patterns". Reaction–diffusion processes form one class of explanation for the embryonic development of animal coats and skin pigmentation. Another reason for the interest in reaction-diffusion systems is that although they represent nonlinear

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

, there are often possibilities for an analytical treatment.Kerner, B. S. and Osipov, V. V. Autosolitons. A New Approach to Problems of Self-Organization and Turbulence,

Kluwer Academic Publishers Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

(1994).

References

{{DEFAULTSORT:Chemical Basis of Morphogenesis 1952 in England 1952 documents Mathematical modeling Parabolic partial differential equations Biological processes Chaos theory Works by English people Alan Turing Mathematics papers

Reaction–diffusion systems

See also

References