What does self-similarity mean?

Definitions for self-similarity
self-sim·i·lar·i·ty

This dictionary definitions page includes all the possible meanings, example usage and translations of the word self-similarity.

Wiktionary

  1. self-similaritynoun

    The property of being self-similar, of having parts that resemble the whole, as a fractal has.

  2. Etymology: From self- and similarity, or from self-similar and -ity.

Wikipedia

  1. Self-similarity

    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 typical property of fractals. 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 distinguished by their fine structure, or detail on arbitrarily small scales. As a counterexample, whereas any portion of a straight line may resemble the whole, further detail is not revealed. A time developing phenomenon is said to exhibit self-similarity if the numerical value of certain observable quantity f ( x , t ) {\displaystyle f(x,t)} measured at different times are different but the corresponding dimensionless quantity at given value of x / t z {\displaystyle x/t^{z}} remain invariant. It happens if the quantity f ( x , t ) {\displaystyle f(x,t)} exhibits dynamic scaling. The idea is just an extension of the idea of similarity of two triangles. Note that two triangles are similar if the numerical values of their sides are different however the corresponding dimensionless quantities, such as their angles, coincide.

Wikidata

  1. Self-similarity

    In 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 statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals. 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 distinguished by their fine structure, or detail on arbitrarily small scales. As a counterexample, whereas any portion of a straight line may resemble the whole, further detail is not revealed.

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Numerology

  1. Chaldean Numerology

    The numerical value of self-similarity in Chaldean Numerology is: 4

  2. Pythagorean Numerology

    The numerical value of self-similarity in Pythagorean Numerology is: 6


Translations for self-similarity

From our Multilingual Translation Dictionary

  • స్వీయ సారూప్యతTelugu
  • Kendi kendine benzerlikTurkish

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"self-similarity." Definitions.net. STANDS4 LLC, 2024. Web. 19 Mar. 2024. <https://www.definitions.net/definition/self-similarity>.

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