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 li ...

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 am ...

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 ...

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 of change in relation to human

experience Experience refers to conscious events in general, more specifically to perceptions, or to the practical knowledge and familiarity that is produced by these conscious processes. Understood as a conscious event in the widest sense, experience involv ...

. 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 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 s ...

* 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 are ...

, 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 oscillation, oscillatory activity in many ways, driven either by mechanisms within individual ne ...

. 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 medium, excitable media. Spiral waves have been observed in various biological systems including systems such as heart ventricula ...

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, sp ...

preparations.

Communication

All

communication Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inqui ...

language Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, and may be conveyed through a variety of ...

, relies on spatiotemporal

encoding In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication ...

of information, producing and

transmitting In electronics and telecommunications, a radio transmitter or just transmitter is an electronic device which produces radio waves with an antenna. The transmitter itself generates a radio frequency alternating current, which is applied to th ...

sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' b ...

variations or any type of

signal In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...

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 eve ...

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 concatenat ...

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 In animal communication, an alarm signal is an antipredator adaptation in the form of signals emitted by social animals in response to danger. Many primates and birds have elaborate alarm calls for warning conspecifics of approaching predators ...

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 Artificial languages are languages of a typically very limited size which emerge either in computer simulations between artificial agents, robot interactions or controlled psychological experiments with humans. They are different from both constr ...

, 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 comput ...

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 pr ...

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

Genetics

As a particular type of language, the "static" (neglecting random transcription errors, recombination and

mutation In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA replication, DNA or viral repl ...

) DNA and its

transcription Transcription refers to the process of converting sounds (voice, music etc.) into letters or musical notes, or producing a copy of something in another medium, including: Genetics * Transcription (biology), the copying of DNA into RNA, the fir ...

pattern over time yields biologically essential s.t. patterns.

Gene regulatory network A gene (or genetic) regulatory network (GRN) is a collection of molecular regulators that interact with each other and with other substances in the cell to govern the gene expression levels of mRNA and proteins which, in turn, determine the fun ...

s 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