Self-Similar

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Self-Similar

When small parts of an object are qualitatively the same, or similar to the whole object. In certain deterministic fractals, like the Sierpinski Triangle, small pieces look the same as the entire object. In random fractals, small increments of time will be statistically similar to larger increments of time. See: Fractal.

Self-Similar

In mathematics, describing a condition in which the parts of an object are substantially the same as its whole. See also: Fractals.
References in periodicals archive ?
To sum up, the central crack azimuth of each well conforms suitably to the fault strike surrounding the borehole, which indicates the apparent self-similarity between fault and fracture layout.
The self-similarity conduct can be clarified by accepting that the structure is made with free radiating dipoles arbitrarily dispersed in space, and each branch of the fractal treeshaped MSA resonated at a wavelength four times its length.
Wlodarczyk, "Self-similarity in jet events following from pp collisions at LHC," Physics Letters B, vol.
The problem has been shown to admit self-similarity of the full MHD fluid flow equations.
In Section 2, we briefly review some classic works: shock filters and self-similarity filtering.
In this paper, the multiscale self-similarity property is leveraged in two ways.
Despite the extensive attention that SFCs have received in the literature and their evident link with fractals, there is no formal definition for their self-similarity. This paper presents a formal conceptualization of the self-similarity adapted to the context SFCs and an efficient computational test to determine whether a specific SFC is self-similar.
Now for the fractals; if you look at figures 2 to 5 below, you see that there is self-similarity across the various frequencies (roughly, alpha, theta, beta, gamma) when you adjust the time frame (adjusted shown and indexed).
Because of self-similarity, fractals are surprisingly easy to create.
In order to search the self-similarity of an image, each distance between patches in the search window is calculated which is computation-intensive and time-consuming.
This variance in self-similarity over data captured by NEAR agent suggests that any detection system designed for these series must be evaluated both against sample data with low Hurst coefficient (i.e.
For example the elastic self-similarity model predicts that stem length scales as the 2/ 3 power of diameter and the geometric self-similarity model, which assumes stems are constructed to resist wind forces with minimal investment in biomass, predicts that stem length is proportional to diameter (Niklas, 1994; Niklas, 1995).