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See all on WikipediaSelf-similarity - Wikipedia
In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a … See more
In mathematics, self-affinity is a feature of a fractal whose pieces are scaled by different amounts in the x- and y-directions. This means that to appreciate the self similarity of these fractal objects, … See more
A compact topological space X is self-similar if there exists a finite set S indexing a set of non-surjective homeomorphisms $${\displaystyle \{f_{s}:s\in S\}}$$ for which See more
The Mandelbrot set is also self-similar around Misiurewicz points.
Self-similarity has important consequences for the design of computer networks, as typical network traffic has self-similar properties. For example, in teletraffic engineering See more• "Copperplate Chevrons" — a self-similar fractal zoom movie
• "Self-Similarity" — New articles about Self-Similarity. Waltz Algorithm
Self-affinity
• Mandelbrot, … See moreWikipedia text under CC-BY-SA license WEBdimensions of self-affine fractals can take distinct values. The original also pioneered in showing that certain difficult new ideas concerning self-affinity are best accepted with …
- Studies of self affinity
Self-affinity - Vocab, Definition, and Must Know Facts - Fiveable
WEBSelf-affinity refers to a property of fractals where a shape or pattern looks similar at different scales but does not maintain exact proportionality across those scales. This means that …
Any one can explain me what is exact difference …
WEBSelf-affinity is distorted self-similarity. In case of self-similarity, the objects is scaled by the same amount in all directions, but in self-affinity scaling is not necessary identical...
WEBIn strict adherence to the scaling principle of economics described in Chapter E2, WBM is self-affine in a statistical sense. This is true with respect to an arbitrary reduction ratio r, …
Self-affinity vs. self-similarity - Mathematics Stack Exchange
WEBNov 7, 2017 · The plot of position against time of a simple random walker is statistically self-affine. If you zoom out, the curve looks flat, if you zoom in, the curve look vertical. In …
Self-affinity - marksmath.org
WEBA self-affine set is simply a set generated by an IFS whose functions are affinities. Although the class of affine functions is still more restrictive that the class of all contractions, there are good reasons to carefully …
SELF-AFFINE FRACTAL SETS, I: THE BASIC FRACTAL …
WEBJan 1, 1986 · The basic self-affinity property is invariance under a map whose diagonal terms can be written as r, r, r G, and r GH with G<1. In addition, using the awkward but …
Gaussian Self-Affinity and Fractals: Globality, The Ear…
WEBGaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, and R/S. Benoît B. Mandelbrot, F.J. Damerau (Assistant), M. Frame (Assistant) ...more. 4.29. 14 ratings1 review. This third volume of the Selected …
Self-affinity Definition & Meaning - YourDictionary
WEBSelf-affinity definition: (mathematics) The condition of a <a>fractal</a> whose pieces are <a>scaled</a> by different amounts in the <i>x</i> and <i>y</i> directions, so that …
Self-Affine Fractals and Fractal Dimension - IOPscience
WEBOct 1, 1985 · First finding: the basic methods of evaluating the global fractal dimension yield 1: globally, a self-affine fractal behaves as it if were not fractal. Second finding: the box …
More Examples of Self-Similarity - users.math.yale.edu
WEBSelf-affine fractals: scaling by different amounts in the x- and y-directions produces fractals that are self-affine, a generalization of self-similar fractals. Circle inversion fracals: we …
Understanding roughness on a small scale: The origin of self-affinity
WEBFeb 28, 2020 · Self-affinity describes a fractal whose pieces are scaled by different amounts depending on the axis. When people think of fractals, they tend to imagine …
Self-Similarity -- from Wolfram MathWorld
WEB5 days ago · Self-similar objects with parameters N and s are described by a power law such as N=s^d, where d=(lnN)/(lns) is the "dimension" of the scaling law, known as the …
Self-similarity and panorama of self-affinity | SpringerLink
WEBThe mathematically ambitious reader who will enter here will simply glance through Section 1, which distinguishes between self-similarity and self-affinity, and Section 2, which is …
WEBThe mathematically ambitious reader who will enter here will simply glance through Section I, which distinguishes between self-Similarity and self-affinity, and Section 2, which is …
Self-affinity dimensions of topography and its implications in ...
WEBOct 1, 2004 · This paper discusses the self-affinity dimensions of landscape surfaces at a short-range scale and the link to morphotectonic features of the young orogenic belts of …
Gaussian Self-Affinity and Fractals - Springer
WEBGaussian Self-Affinity and Fractals. Globality, The Earth, 1/f Noise, and R/S. Book. © 2002. Overview. Authors: Benoit Mandelbrot. 3rd volume in the series of Mandelbrot's Selecta. …
Statistical self-affinity, fractal dimension, and geologic ...
WEBDec 1, 1997 · Statistical self-affinity means that a statistical parameter matches that of the original function upon resampling only if a proper resealing is performed. The statistical …
self-affinity - Wiktionary, the free dictionary
WEBAug 18, 2024 · (mathematics) The condition of a fractal whose pieces are scaled by different amounts in the x and y directions, so that self-similarity becomes apparent only after an …
A new first: Scientists mimic nature's self-affinity using computer ...
WEBMar 19, 2019 · The study shows that the development of the self-affine morphology is due to smoothing and re-roughening mechanisms via subsurface crack propagation and third …
Self-affinity in financial asset returns - ScienceDirect
WEBSep 1, 2012 · Stock returns may exhibit the weaker property of self-affinity. After the application of a suitable rescaling transformation, which takes the form of a single non …
Self-assembling nanoparticle engineered from the ... - Nature
WEB2 days ago · The engineered ferritinophagy (Fagy)-tag peptide demonstrate significantly enhanced binding affinity to the 24-mer ferritin nanoparticle, enabling efficient antigen …
Self-Similarity and Self-Affinity | SpringerLink
WEBAbstract. The probability distribution for Brownian motion satisfies the scaling relations given by equations (9.8) and (9.10), analogous to the scaling relations (2.12), (2.13) and …
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