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Anisotropy (ˌænaɪˈsɒtrəpi) is the property of being directionally dependent, as opposed to isotropy
Isotropy is uniformity in all orientations; it is derived from the Greek iso and tropos . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix an, hence anisotropy. Anisotropy is also used to describe situations where properties vary...

, which implies identical properties in all directions. It can be defined as a difference, when measured along different axes, in a material's physical or mechanical properties (absorbance, refractive index, conductivity, tensile strength, etc.) An example of anisotropy is the light coming through a polarizer
A polarizer is an optical filter that passes light of a specific polarization and blocks waves of other polarizations. It can convert a beam of light of undefined or mixed polarization into a beam with well-defined polarization. The common types of polarizers are linear polarizers and circular...

. An example of an anisotropic material is wood, which is easier to split along its grain
Wood grain
In speaking of wood the term grain refers to the alternating regions of relatively darker and lighter wood resulting from the differing growth parameters occurring in different seasons . The term is used in several ways. Perhaps most important is that in woodworking techniques...

 than against it.

Computer graphics

In the field of computer graphics
Computer graphics
Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....

, an anisotropic surface will change in appearance as it is rotated about its geometric normal
Surface normal
A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...

, as is the case with velvet
Velvet is a type of woven tufted fabric in which the cut threads are evenly distributed,with a short dense pile, giving it a distinctive feel.The word 'velvety' is used as an adjective to mean -"smooth like velvet".-Composition:...


Anisotropic filtering
Anisotropic filtering
In 3D computer graphics, anisotropic filtering is a method of enhancing the image quality of textures on surfaces that are at oblique viewing angles with respect to the camera where the projection of the texture appears to be non-orthogonal In 3D computer graphics, anisotropic filtering...

 (AF) is a method of enhancing the image quality of textures on surfaces that are far away and steeply angled with respect to the point of view. Older techniques, such as bilinear
Bilinear filtering
Bilinear filtering is a texture filtering method used to smooth textures when displayed larger or smaller than they actually are.Most of the time, when drawing a textured shape on the screen, the texture is not displayed exactly as it is stored, without any distortion...

 and trilinear filtering
Trilinear filtering
Trilinear filtering is an extension of the bilinear texture filtering method, which also performs linear interpolation between mipmaps.Bilinear filtering has several weaknesses that make it an unattractive choice in many cases: using it on a full-detail texture when scaling to a very small size...

, do not take into account the angle a surface is viewed from, which can result in aliasing
In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...

 or blurring of textures. By reducing detail in one direction more than another, these effects can be reduced.


A chemical anisotropic filter
Filter (chemistry)
In chemistry and common usage, a filter is a device that is designed to physically block certain objects or substances while letting others through. Filters are often used to remove solid substances suspended in fluids, for example to remove air pollution, to make water drinkable, and to prepare...

, as used to filter particles, is a filter with increasingly smaller interstitial spaces in the direction of filtration so that the proximal region
Region is most commonly found as a term used in terrestrial and astrophysics sciences also an area, notably among the different sub-disciplines of geography, studied by regional geographers. Regions consist of subregions that contain clusters of like areas that are distinctive by their uniformity...

s filter out larger particles and distal regions increasingly remove smaller pales, resulting in greater flow-through and more efficient filtration.

In NMR spectroscopy
NMR spectroscopy
Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy, is a research technique that exploits the magnetic properties of certain atomic nuclei to determine physical and chemical properties of atoms or the molecules in which they are contained...

, the orientation of nuclei with respect to the applied magnetic field determines their chemical shift
Chemical shift
In nuclear magnetic resonance spectroscopy, the chemical shift is the resonant frequency of a nucleus relative to a standard. Often the position and number of chemical shifts are diagnostic of the structure of a molecule...

. In this context, anisotropic systems refer to the electron distribution of molecules with abnormally high electron density, like the pi system of benzene
Benzene is an organic chemical compound. It is composed of 6 carbon atoms in a ring, with 1 hydrogen atom attached to each carbon atom, with the molecular formula C6H6....

. This abnormal electron density affects the applied magnetic field and causes the observed chemical shift to change.

In fluorescence spectroscopy
Fluorescence spectroscopy
Fluorescence spectroscopy aka fluorometry or spectrofluorometry, is a type of electromagnetic spectroscopy which analyzes fluorescence from a sample. It involves using a beam of light, usually ultraviolet light, that excites the electrons in molecules of certain compounds and causes them to emit...

, the fluorescence anisotropy
Fluorescence anisotropy
Fluorescence anisotropy is the phenomenon where the light emitted by a fluorophore has unequal intensities along different axes of polarization...

, calculated from the polarization properties of fluorescence from samples excited with plane-polarized light, is used, e.g., to determine the shape of a macromolecule.
Anisotropy measurements reveal the average angular displacement of the fluorophore that occurs between absorption and subsequent emission of a photon.

Real-world imagery

Images of a gravity-bound or man-made environment are particularly anisotropic in the orientation domain, with more image structure located at orientations parallel with or orthogonal to the direction of gravity (vertical and horizontal).


Cosmologists use the term to describe the uneven temperature distribution of the cosmic microwave background radiation
Cosmic microwave background radiation
In cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....

. There is evidence for a so-called "Axis of Evil" in the early Universe that is at odds with the currently favored theory of rapid expansion after the Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

. Cosmic anisotropy has also been seen in the alignment of galaxies' rotation axes and polarisation angles of quasars.

Physicists use the term anisotropy to describe direction-dependent properties of materials. Magnetic anisotropy
Magnetic anisotropy
Magnetic anisotropy is the direction dependence of a material's magnetic properties. In the absence of an applied magnetic field, a magnetically isotropic material has no preferential direction for its magnetic moment while a magnetically anisotropic material will align its moment with one of the...

, for example, may occur in a plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

, so that its magnetic field is oriented in a preferred direction. Plasmas may also show "filamentation" (such as that seen in lightning
Lightning is an atmospheric electrostatic discharge accompanied by thunder, which typically occurs during thunderstorms, and sometimes during volcanic eruptions or dust storms...

 or a plasma globe) that is directional.

An anisotropic liquid is one which has the fluidity of a normal liquid, but has an average structural order relative to each other along the molecular axis, unlike water or chloroform
Chloroform is an organic compound with formula CHCl3. It is one of the four chloromethanes. The colorless, sweet-smelling, dense liquid is a trihalomethane, and is considered somewhat hazardous...

, which contain no structural ordering of the molecules. Liquid crystals are examples of anisotropic liquids.

Some materials conduct heat
Heat conduction
In heat transfer, conduction is a mode of transfer of energy within and between bodies of matter, due to a temperature gradient. Conduction means collisional and diffusive transfer of kinetic energy of particles of ponderable matter . Conduction takes place in all forms of ponderable matter, viz....

 in a way that is isotropic, that is independent of spatial orientation around the heat source. It is more common for heat conduction to be anisotropic, which implies that detailed geometric modeling of typically diverse materials being thermally managed is required. The materials used to transfer and reject heat from the heat source in electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

 are often anisotropic.

Many crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

s are anisotropic to light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

 ("optical anisotropy"), and exhibit properties such as birefringence
Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...

. Crystal optics
Crystal optics
Crystal optics is the branch of optics that describes the behaviour of light in anisotropic media, that is, media in which light behaves differently depending on which direction the light is propagating. The index of refraction depends on both composition and crystal structure and can be...

 describes light propagation in these media. An "axis of anisotropy" is defined as the axis along which isotropy is broken (or an axis of symmetry, such as normal to crystalline layers). Some materials can have multiple such optical axes
Optical axis
An optical axis is a line along which there is some degree of rotational symmetry in an optical system such as a camera lens or microscope.The optical axis is an imaginary line that defines the path along which light propagates through the system...


Geology and Geophysics

Seismic anisotropy
Seismic anisotropy
Seismic anisotropy is a term used in seismology to describe the directional dependence of seismic wavespeed in a medium within the Earth.- Crustal Anisotropy :...

 is the variation of seismic wavespeed with direction. Seismic anisotropy is an indicator of long range order in a material, where features smaller than the seismic wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

 (e.g., crystals, cracks, pores, layers or inclusions) have a dominant alignment. This alignment leads to a directional variation of elasticity
Elasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....

 wavespeed. Measuring the effects of anisotropy in seismic data can provide important information about processes and mineralogy in the Earth; indeed, significant seismic anisotropy has been detected in the Earth's crust
Crust may refer to:* Crust * The Crust, television seriesPhysical sciences:* Crust , at least continent-wide structure* Soil crust, local biology-sensitive structureFood:* Crust, dense surface layer of bread...

, mantle
Mantle (geology)
The mantle is a part of a terrestrial planet or other rocky body large enough to have differentiation by density. The interior of the Earth, similar to the other terrestrial planets, is chemically divided into layers. The mantle is a highly viscous layer between the crust and the outer core....

 and inner core
Inner core
The inner core of the Earth, its innermost hottest part as detected by seismological studies, is a primarily solid ball about in radius, or about 70% that of the Moon...


Geological formations with distinct layers of sedimentary material can exhibit electrical anisotropy; electrical conductivity in one direction (e.g. parallel to a layer), is different from that in another (e.g. perpendicular to a layer). This property is used in the gas and oil exploration
Oil exploration
Hydrocarbon exploration is the search by petroleum geologists and geophysicists for hydrocarbon deposits beneath the Earth's surface, such as oil and natural gas...

 industry to identify hydrocarbon
In organic chemistry, a hydrocarbon is an organic compound consisting entirely of hydrogen and carbon. Hydrocarbons from which one hydrogen atom has been removed are functional groups, called hydrocarbyls....

-bearing sands in sequences of sand
Sand is a naturally occurring granular material composed of finely divided rock and mineral particles.The composition of sand is highly variable, depending on the local rock sources and conditions, but the most common constituent of sand in inland continental settings and non-tropical coastal...

 and shale
Shale is a fine-grained, clastic sedimentary rock composed of mud that is a mix of flakes of clay minerals and tiny fragments of other minerals, especially quartz and calcite. The ratio of clay to other minerals is variable. Shale is characterized by breaks along thin laminae or parallel layering...

. Sand-bearing hydrocarbon assets have high resistivity
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...

 (low conductivity), whereas shales have lower resistivity. Formation evaluation
Formation evaluation
In petroleum exploration and development, formation evaluation is used to determine the ability of a borehole to produce petroleum. Essentially, it is the process of "recognizing a commercial well when you drill one"....

 instruments measure this conductivity/resistivity and the results are used to help find oil and gas wells.

The hydraulic conductivity
Hydraulic conductivity
Hydraulic conductivity, symbolically represented as K, is a property of vascular plants, soil or rock, that describes the ease with which water can move through pore spaces or fractures. It depends on the intrinsic permeability of the material and on the degree of saturation...

 of aquifer
An aquifer is a wet underground layer of water-bearing permeable rock or unconsolidated materials from which groundwater can be usefully extracted using a water well. The study of water flow in aquifers and the characterization of aquifers is called hydrogeology...

s is often anisotropic for the same reason. When calculating groundwater flow to drains
Drainage is the natural or artificial removal of surface and sub-surface water from an area. Many agricultural soils need drainage to improve production or to manage water supplies.-Early history:...

 or to wells
Water well
A water well is an excavation or structure created in the ground by digging, driving, boring or drilling to access groundwater in underground aquifers. The well water is drawn by an electric submersible pump, a trash pump, a vertical turbine pump, a handpump or a mechanical pump...

, the difference between horizontal and vertical permeability is to be taken into account otherwise the results may be subject to error.

Most common rock-forming mineral
A mineral is a naturally occurring solid chemical substance formed through biogeochemical processes, having characteristic chemical composition, highly ordered atomic structure, and specific physical properties. By comparison, a rock is an aggregate of minerals and/or mineraloids and does not...

s are anisotropic, including quartz
Quartz is the second-most-abundant mineral in the Earth's continental crust, after feldspar. It is made up of a continuous framework of SiO4 silicon–oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall formula SiO2. There are many different varieties of quartz,...

 and feldspar
Feldspars are a group of rock-forming tectosilicate minerals which make up as much as 60% of the Earth's crust....

. Anisotropy in minerals is most reliably seen in their optical properties
Optical mineralogy
Optical mineralogy is the study of minerals and rocks by measuring their optical properties. Most commonly, rock and mineral samples are prepared as thin sections or grain mounts for study in the laboratory with a petrographic microscope...

. An example of an isotropic mineral is garnet
The garnet group includes a group of minerals that have been used since the Bronze Age as gemstones and abrasives. The name "garnet" may come from either the Middle English word gernet meaning 'dark red', or the Latin granatus , possibly a reference to the Punica granatum , a plant with red seeds...


Medical acoustics

Anisotropy is also a well-known property in medical ultrasound imaging describing a different resulting echogenicity
Echogenicity is the ability to bounce an echo, e.g. return the signal in ultrasound examinations. In other words, Echogenicity is higher when the surface bouncing the sound echo reflects increased sound waves. It could be increased by intravenously administering gas-filled microbubble contrast...

 of soft tissues, such as tendons, when the angle of the transducer is changed. Tendon fibers appear hyperechoic (bright) when the transducer is perpendicular to the tendon, but can appear hypoechoic (darker) when the transducer is angled obliquely. This can be a source of interpretation error for inexperienced practitioners. In diffusion tensor imaging, anisotropy alterations may reflect diffusion changes of water in the brain, particularly in the white matter
White matter
White matter is one of the two components of the central nervous system and consists mostly of myelinated axons. White matter tissue of the freshly cut brain appears pinkish white to the naked eye because myelin is composed largely of lipid tissue veined with capillaries. Its white color is due to...


Material science and engineering

Anisotropy, in Material Science, is a material’s directional dependence of a physical property. Most materials exhibit anisotropic behavior. An example would be the dependence of Young's modulus
Young's modulus
Young's modulus is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. In solid mechanics, the slope of the stress-strain...

 on the direction of load.
Anisotropy in polycrystalline materials can also be due to certain texture
Texture (crystalline)
In materials science, texture is the distribution of crystallographic orientations of a polycrystalline sample. A sample in which these orientations are fully random is said to have no texture. If the crystallographic orientations are not random, but have some preferred orientation, then the...

 patterns which are often produced during manufacturing of the material. In the case of rolling, "stringers" of texture are produced in the direction of rolling, which can lead to vastly different properties in the rolling and transverse directions.
Some materials, such as wood and fibre-reinforced composites
Composite material
Composite materials, often shortened to composites or called composition materials, are engineered or naturally occurring materials made from two or more constituent materials with significantly different physical or chemical properties which remain separate and distinct at the macroscopic or...

 are very anisotropic, being much stronger along the grain/fibre than across it. Metals and alloys tend to be more isotropic, though they can sometimes exhibit significant anisotropic behaviour. This is especially important in processes such as deep-drawing
Stamping (metalworking)
Stamping includes a variety of sheet-metal forming manufacturing processes, such as punching using a machine press or stamping press, blanking, embossing, bending, flanging, and coining. This could be a single stage operation where every stroke of the press produce the desired form on the sheet...


Wood is a naturally anisotropic material. Its properties vary widely when measured with the growth grain or against it. For example, wood's strength and hardness will be different for the same sample if measured in differing orientation.


Anisotropic etching techniques (such as deep reactive ion etching
Deep reactive ion etching
Deep reactive-ion etching is a highly anisotropic etch process used to create deep penetration, steep-sided holes and trenches in wafers/substrates, typically with high aspect ratios...

) are used in microfabrication processes to create well defined microscopic features with a high aspect ratio
Aspect ratio
The aspect ratio of a shape is the ratio of its longer dimension to its shorter dimension. It may be applied to two characteristic dimensions of a three-dimensional shape, such as the ratio of the longest and shortest axis, or for symmetrical objects that are described by just two measurements,...

. These features are commonly used in MEMS
Microelectromechanical systems
Microelectromechanical systems is the technology of very small mechanical devices driven by electricity; it merges at the nano-scale into nanoelectromechanical systems and nanotechnology...

 and microfluidic devices, where the anisotropy of the features is needed to impart desired optical, electrical, or physical properties to the device. Anisotropic etching could also refer to certain chemical etchants which are etching a certain material preferentially over certain crystallographic planes (e.g., KOH etching of silicon
Silicon is a chemical element with the symbol Si and atomic number 14. A tetravalent metalloid, it is less reactive than its chemical analog carbon, the nonmetal directly above it in the periodic table, but more reactive than germanium, the metalloid directly below it in the table...

 [100] produces pyramid-like structures)


Diffusion tensor imaging is an MRI
Magnetic resonance imaging
Magnetic resonance imaging , nuclear magnetic resonance imaging , or magnetic resonance tomography is a medical imaging technique used in radiology to visualize detailed internal structures...

 technique that involves measuring the fractional anisotropy of the random motion (Brownian motion
Brownian motion
Brownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...

) of water molecules in the brain. Water molecules located in fiber tracts
White matter
White matter is one of the two components of the central nervous system and consists mostly of myelinated axons. White matter tissue of the freshly cut brain appears pinkish white to the naked eye because myelin is composed largely of lipid tissue veined with capillaries. Its white color is due to...

are more likely to be anisotropic, since they are restricted in their movement (they move more in the dimension parallel to the fiber tract rather than in the two dimensions orthogonal to it), whereas water molecules dispersed in the rest of the brain have less restricted movement and therefore display more isotropy. This difference in fractional anisotropy is exploited to create a map of the fiber tracts in the brains of the individual.

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