Spatiotemporal patterns are

pattern A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated l ...

s that occur in a wide range of natural phenoma and are characterized by a spatial and a temporal patterning. The general rules of

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 ...

hold. In contrast to "static", pure spatial patterns, the full complexity of spatiotemporal patterns can only be recognized over time. Any kind of

traveling wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (re ...

is a good example of a spatiotemporal pattern. Besides the shape and

amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of ampl ...

of the wave (spatial part), its time-varying position (and possibly shape) in space is an essential part of the entire pattern. The distinction between spatial and spatio-temporal patterns in

nature Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are p ...

is not clear-cut because a static, invariable pattern will never occur in the strict sense. Even rock formations will slowly change on a time-scale of 10s of millions of years, therefore the distinction lies in the

time scale Time scale may refer to: *Time standard, a specification of either the rate at which time passes, points in time, or both *A duration or quantity of time: **Orders of magnitude (time) as a power of 10 in seconds; **A specific unit of time *Geologi ...

of change in relation to human experience. Already the snapshot state of a dune will usually be taken as an example of a purely spatial pattern although this is clearly not the case. It is thus apt to say that spatiotemporal patterns in nature are the rule rather than the exception.

Physics

Many

hydrodynamical In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...

systems show s.t. pattern formation: *

Rayleigh–Bénard convection In fluid thermodynamics, Rayleigh–Bénard convection is a type of natural convection, occurring in a planar horizontal layer of fluid heated from below, in which the fluid develops a regular pattern of convection cells known as Bénard cells. ...

Taylor–Couette flow In fluid dynamics, the Taylor–Couette flow consists of a viscous fluid confined in the gap between two rotating cylinders. For low angular velocities, measured by the Reynolds number ''Re'', the flow is steady and purely azimuthal. This basic ...

* Liquid crystal instabilities

Chemistry

Any type of reaction–diffusion system that produces spatial patterns will also, due to the time-dependency of both reactions and diffusion, produce spatiotemporal patterns.

Biology

Neurobiology

Neural networks, both

artificial Artificiality (the state of being artificial or manmade) is the state of being the product of intentional human manufacture, rather than occurring naturally through processes not involving or requiring human activity. Connotations Artificiality ...

and

natural Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans ar ...

, produce a virtually unbounded variety of s.t. patterns, both in

sensory perception Perception () is the organization, identification, and interpretation of sensory information in order to represent and understand the presented information or environment. All perception involves signals that go through the nervous system ...

, learning, thinking and reasoning as well as in

spontaneous activity Neural oscillations, or brainwaves, are rhythmic or repetitive patterns of neural activity in the central nervous system. Neural tissue can generate oscillatory activity in many ways, driven either by mechanisms within individual neurons or by ...

. It has for example been demonstrated that

spiral wave Spiral waves are travelling waves that rotate outward from a center in a spiral. They are a feature of many excitable media. Spiral waves have been observed in various biological systems including systems such as heart ventricular fibrillation, ...

s, signatures of many excitable systems can occur in

neocortical The neocortex, also called the neopallium, isocortex, or the six-layered cortex, is a set of layers of the mammalian cerebral cortex involved in higher-order brain functions such as sensory perception, cognition, generation of motor commands, s ...

preparations.

Communication

All communication, language, relies on spatiotemporal encoding of information, producing and transmitting sound variations or any type of signal i.e. single building blocks of information that are varied over time. -Even though

written language A written language is the representation of a spoken or gestural language by means of a writing system. Written language is an invention in that it must be taught to children, who will pick up spoken language or sign language by exposure even i ...

appears to exist only as a (2D) spatial

concatenation In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In certain formalisations of concatena ...

of letters - strings, it must be decoded sequentially over time. Any kind of language that is understood by organisms is thus eventually a transcoding of neural s.t. signals and will - in successful communication - evoke similar patterns of neural activity in the recipient as they existed in the sender. For example, the warning call of a bird when it perceives a predator will produce a similar type and degree of alarmedness (eventually a certain kind of neural activity pattern) in other individuals even though they have not yet seen or heard the potential attacker. Even artificial languages, e.g.

computer language A computer language is a formal language used to communicate with a computer. Types of computer languages include: * Construction language – all forms of communication by which a human can specify an executable problem solution to a compu ...

s, are not read and interpreted in one step, but sequentially, thus, their meaningfully arranged vocabulary (e.g. "

computer code A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These progra ...

") can be seen as a s.t. pattern.

Genetics

As a particular type of language, the "static" (neglecting random

transcription error A transcription error is a specific type of data entry error that is commonly made by human operators or by optical character recognition (OCR) programs. Human transcription errors are commonly the result of typographical mistakes; putting one’ ...

s, recombination and mutation) DNA and its transcription pattern over time yields biologically essential s.t. patterns. Gene regulatory networks are responsible for regulation the time course of gene expression level which can be analyzed using

expression profiling In the field of molecular biology, gene expression profiling is the measurement of the activity (the expression) of thousands of genes at once, to create a global picture of cellular function. These profiles can, for example, distinguish between c ...

Literature

References

{{Reflist Information theory Pattern formation Space and time