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- Self-similarity refers to the property where an object or process is similar to a part of itself, either exactly or approximately. In mathematics, self-similar objects have the same shape as one or more of their parts, and many real-world phenomena, such as coastlines, exhibit statistical self-similarity at different scales. In data analysis, self-similarity can be represented using matrices or other measures12. Self-similar processes in stochastic modeling behave the same when viewed at different degrees of magnification or scales3.Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.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.en.wikipedia.org/wiki/Self-similarityIn data analysis, the self-similarity matrix is a graphical representation of similar sequences in a data series. Similarity can be explained by different measures, like spatial distance (distance matrix), correlation, or comparison of local histograms or spectral properties (e.g. IXEGRAM).en.wikipedia.org/wiki/Self-similarity_matrixSelf-similar processes are types of stochastic processes that exhibit the phenomenon of self-similarity. A self-similar phenomenon behaves the same when viewed at different degrees of magnification, or different scales on a dimension (space or time).en.wikipedia.org/wiki/Self-similar_process
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Self-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 Self-similar solution - Wikipedia
In the study of partial differential equations, particularly in fluid dynamics, a self-similar solution is a form of solution which is similar to itself if the independent and dependent variables are appropriately scaled. Self-similar solutions appear whenever the problem lacks a characteristic length or time scale (for example, the Blasius boundary layer of an infinite plate, but not of a finite-length plate). These include, for example, the Blasius boundary layer or the Sedov–Taylor shell.
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Self-similar process - Wikipedia
WEBA self-similar phenomenon behaves the same when viewed at different degrees of magnification, or different scales on a dimension (space or time). Self-similar processes …
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Self-similarity - Simple English Wikipedia, the free encyclopedia
WEBSomething is self-similar if it is similar (or very close) to a part of itself. [1] For example, the Mandelbrot set is self-similar as it contains an infinite number of almost exact copies of …
Self-similarity - Wikipedia, the free encyclopedia
WEBJan 22, 2009 · 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 …
Self-similarity - WikiMili, The Best Wikipedia Reader
WEBSep 16, 2023 · This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this …
Self-similarity: Properties and Applications - Sera Markoff
WEBMar 28, 2021 · In mathematics, self-similarity describes the property of an object if a part of it resembles the whole object. In the aforementioned nursery rhyme, the story the old monk tells is the same as the rhyme itself.
Self-similarity | geometry | Britannica
WEBA self-similar object is one whose component parts resemble the whole. This reiteration of details or patterns occurs at progressively smaller scales and can, in the case of …
What is the difference between scale invariance and self-similarity?
WEBA self-similar transformation like the one producing the Cantor set or the Sierpinski triangle proceeds by discrete stages. The fractal which is the limit when the number of …
Self-similarity matrix - Wikipedia
WEBIn data analysis, the self-similarity matrix is a graphical representation of similar sequences in a data series. Similarity can be explained by different measures, like spatial distance ( …
Self-similarity Definition & Meaning - Merriam-Webster
WEBThe meaning of SELF-SIMILARITY is the quality or state of having an appearance that is invariant upon being scaled larger or smaller. How to use self-similarity in a sentence.
Self-similarity - Wikiwand / articles
WEBIn mathematics, a self-similar object is exactly or approximately similar to a part of itself. Many objects in the real world, such as coastlines, are statistic...
Is there any mathematical proof of fractal self-similarity?
WEBJul 6, 2017 · From 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 …
Self-Similarity -- from Wolfram MathWorld
WEBAug 22, 2024 · An object is said to be self-similar if it looks "roughly" the same on any scale. Fractals are a particularly interesting class of self-similar objects.
What is Scale invariance? - Physics Stack Exchange
WEBScale invariance can be thought of as ' self-similarity '. What this really means is that regardless of how much you zoom into or out of an object (be it a function, or a physical …
On the Self-similarity of Wikipedia Talks: a Combined Discourse ...
WEBAccording to these findings, we distinguish two sorts of self-similarity of Wikipedia’s discussion space: horizontally, regarding thematically demarcated subparts of this …
Scale invariance - Wikipedia
WEBA closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilations. It is also possible for the probability distributions of …
Category:Self-similarity - Wikimedia Commons
WEBCategory. : Self-similarity. From Wikimedia Commons, the free media repository. self-similarity. property of an object in which the whole is exact or roughly similar to a part …
self-similarity - Wiktionary, the free dictionary
WEBself - similarity ( countable and uncountable, plural self-similarities) The property of being self-similar, of having parts that resemble the whole, as a fractal has.
Self-Similarity of Network Data Analysis - Wikipedia
WEBA self-similar process is one way of modeling network data dynamics with such a long range correlation. This article defines and describes network data transfer dynamics in …
自相似 - 维基百科,自由的百科全书
WEB數學 分支 分形幾何 中,如果一個物體 自我相似 (Self-similarity),表示它和它本身的一部分完全或是幾乎 相似 。. 若說一個曲線自我相似,即每部分的曲線有一小塊和它相似 …
Coastline paradox - Wikipedia
WEBA key property of some fractals is self-similarity; that is, at any scale the same general configuration appears. A coastline is perceived as bays alternating with promontories.
Self-similarity — Wikipedia Republished // WIKI 2
WEBIn 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 …