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Each iteration of the Sierpinski triangle contains triangles related to the next iteration by a scale factor of 1/2. In affine geometry, uniform scaling (or isotropic scaling [1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically).
Anisotropy (/ ˌ æ n aɪ ˈ s ɒ t r ə p i, ˌ æ n ɪ-/) is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement.
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
This definition is also used in geology and mineralogy. Glass and metals are examples of isotropic materials. [3] Common anisotropic materials include wood (because its material properties are different parallel to and perpendicular to the grain) and layered rocks such as slate.
Fractional anisotropy (FA) is a scalar value between zero and one that describes the degree of anisotropy of a diffusion process. A value of zero means that diffusion is isotropic, i.e. it is unrestricted (or equally restricted) in all directions.
The geometric transformation represented by a diagonalizable matrix is an inhomogeneous dilation (or anisotropic scaling). That is, it can scale the space by a different amount in different directions. The direction of each eigenvector is scaled by a factor given by the corresponding eigenvalue.
Anisotropic diffusion can be used to remove noise from digital images without blurring edges. With a constant diffusion coefficient, the anisotropic diffusion equations reduce to the heat equation which is equivalent to Gaussian blurring. This is ideal for removing noise but also indiscriminately blurs edges too.
Here = ¯ is the Reynolds stress anisotropy tensor, is the rate of strain term for the mean velocity field and is the rate of rotation term for the mean velocity field. By convention, C 2 , C 3 , C 4 {\displaystyle C_{2},C_{3},C_{4}} are the coefficients of the rapid pressure strain correlation model.