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 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 c ...

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 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 is an inherent character or constitution, particularly of the Ecosphere (planetary), ecosphere or the universe as a whole. In this general sense nature refers to the Scientific law, laws, elements and phenomenon, phenomena of the physic ...

is not clear-cut because a static, invariable pattern will never occur in the strict sense. Even

rock formation A rock formation is an isolated, scenic, or spectacular surface rock (geology), rock outcrop. Rock formations are usually the result of weathering and erosion sculpting the existing rock. The term ''rock Geological formation, formation ...

s will slowly change on a time-scale of tens of millions of years, therefore the distinction lies in the time scale of change in relation to human

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

. Already the snapshot state of a

dune A dune is a landform composed of wind- or water-driven sand. It typically takes the form of a mound, ridge, or hill. An area with dunes is called a dune system or a dune complex. A large dune complex is called a dune field, while broad, flat ...

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 *

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 laminar ...

Liquid crystal Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal can flow like a liquid, but its molecules may be oriented in a common direction as i ...

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, anthropogenic, or man-made) is the state of being the product of intentional human manufacture, rather than occurring naturally through processes not involving or requiring human activity. Connotati ...

and

natural Nature is an inherent character or constitution, particularly of the ecosphere or the universe as a whole. In this general sense nature refers to the laws, elements and phenomena of the physical world, including life. Although humans are part ...

, 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 syste ...

, learning, thinking and reasoning as well as in spontaneous activity. It has for example been demonstrated that spiral waves, 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 sense, sensory perception, cognition, generation of motor cortex ...

preparations.

Communication

All

communication Communication is commonly defined as the transmission of information. Its precise definition is disputed and there are disagreements about whether Intention, unintentional or failed transmissions are included and whether communication not onl ...

language Language is a structured system of communication that consists of grammar and vocabulary. It is the primary means by which humans convey meaning, both in spoken and signed language, signed forms, and may also be conveyed through writing syste ...

, relies on spatiotemporal

encoding In communications and Data processing, information processing, code is a system of rules to convert information—such as a letter (alphabet), letter, word, sound, image, or gesture—into another form, sometimes data compression, shortened or ...

of information, producing and transmitting

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'' by the br ...

variations or any type of

signal A signal is both the process and the result of transmission of data over some media accomplished by embedding some variation. Signals are important in multiple subject fields including signal processing, information theory and biology. In ...

i.e. single building blocks of information that are varied over time. -Even though

written language A written language is the representation of a language by means of writing. This involves the use of visual symbols, known as graphemes, to represent linguistic units such as phonemes, syllables, morphemes, or words. However, written language is ...

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 formalizations of concatenati ...

of letters -

string String or strings may refer to: *String (structure), a long flexible structure made from threads twisted together, which is used to tie, bind, or hang other objects Arts, entertainment, and media Films * ''Strings'' (1991 film), a Canadian anim ...

s, 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: * Software construction#Construction languages, Construction language – all forms of communication by which a human can Comput ...

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

computer code Computer code may refer to: *Source code *Machine code *Bytecode Bytecode (also called portable code or p-code) is a form of instruction set designed for efficient execution by a software interpreter. Unlike human-readable source code, byte ...

") 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 or viral replication, ...

)

DNA Deoxyribonucleic acid (; DNA) is a polymer composed of two polynucleotide chains that coil around each other to form a double helix. The polymer carries genetic instructions for the development, functioning, growth and reproduction of al ...

and its transcription 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 fu ...

s are responsible for regulation the time course of

gene expression Gene expression is the process (including its Regulation of gene expression, regulation) by which information from a gene is used in the synthesis of a functional gene product that enables it to produce end products, proteins or non-coding RNA, ...

level which can be analyzed using expression profiling.

Crime

Criminals show spatiotemporal patterns when planning and executing their activities that may be used to predict their future behaviour. Temporal patterns may apply to preferred times when crimes are committed. Spatial patterns can be identified in potential targets and routes for criminal activities. Spatial patterns may be used to identify the most likely locations for crimes to occur, or to identify potential escape routes. In addition, criminals often use temporal and spatial patterns to hide their activities, such as by committing crimes in areas with low population density or in areas with limited surveillance. By understanding spatiotemporal patterns in relation to crime,

law enforcement Law enforcement is the activity of some members of the government or other social institutions who act in an organized manner to enforce the law by investigating, deterring, rehabilitating, or punishing people who violate the rules and norms gove ...

and

crime prevention Crime prevention refers to strategies and measures that seek to reduce the risk of crime occurring by intervening before a crime has been committed. It encompasses many approaches, including developmental, situational, community-based and crimin ...

professionals can develop strategies to better prevent and respond to criminal activities. For example, law enforcement can use spatiotemporal patterns to identify crime hot spots and to determine the most effective strategies for responding to these areas. In addition, law enforcement and crime prevention professionals can use spatiotemporal patterns to identify and monitor potential suspects or areas of criminal activity.

Literature

References

{{Reflist Information theory Pattern formation Space and time