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Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape. The non-trivial similarity evident in fractals is ...
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).
Autoscaling, also spelled auto scaling or auto-scaling, and sometimes also called automatic scaling, is a method used in cloud computing that dynamically adjusts the amount of computational resources in a server farm - typically measured by the number of active servers - automatically based on the load on the farm. For example, the number of ...
Subtracting the mean before multiplication yields the auto-covariance ... of the autocorrelation as a correlation provides a scale-free measure of the ...
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions (and ) that produces a third function (). The term convolution refers to both the resulting function and to the process of computing it.
A powerful tool in physics is the concept of dimensional analysis and scaling laws. By examining the physical effects present in a system, we may estimate their size and hence which, for example, might be neglected. In some cases, the system may not have a fixed natural length or time scale, while the solution depends on space or time.
Scale analysis (or order-of-magnitude analysis) is a powerful tool used in the mathematical sciences for the simplification of equations with many terms. First the approximate magnitude of individual terms in the equations is determined.
Image scaling can be interpreted as a form of image resampling or image reconstruction from the view of the Nyquist sampling theorem.According to the theorem, downsampling to a smaller image from a higher-resolution original can only be carried out after applying a suitable 2D anti-aliasing filter to prevent aliasing artifacts.