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词汇 self-similar
释义

Definition of self-similar in English:

self-similar

adjective
Mathematics
  • (of an object or set of objects) similar to itself at a different time, or to a copy of itself on a different scale.

    〔数〕(物体,一组物体)自型的

    the result has the property of being self-similar, a magnified portion looks like the whole
    Example sentencesExamples
    • He noted that the body is full of fractals, self-similar repeating patterns at different scales, just as nature is full of fractals.
    • We would like to understand the projections of self-similar sets in the plane.
    • Since the creature does not change shape, rather simply grows larger, the most efficient way to do this is for its shell to grow in the self-similar form of a logarithmic spiral.
    • Indeed, nature features many irregular shapes that are self-similar - that repeat themselves on different scales within the same object.
    • A fractal is a mathematical object that is self-similar irrespective of scale.

Derivatives

  • self-similarity

  • noun
    Mathematics
    • For example, a number of musicians have played with the fractal notion of self-similarity, in which each smaller piece of a structure is a miniature version of the larger structure.
      Example sentencesExamples
      • The results are visually more subtle than the instantly identifiable, artificial patterns generated using exact self-similarity, where the patterns repeat exactly at different magnifications.
      • Nature builds its fractals using statistical self-similarity: the patterns observed at different magnifications, although not identical, are described by the same statistics.
      • The principle of self-similarity that underlies fractal geometry, crucial to the scientific understanding of nature, is reflected in much two-dimensional South African art, including beadwork and mural arts among the Basotho.
      • However, stems tapering according to stress self-similarity had the larger factors of safety near their base compared to those tapering according to geometric or elastic self-similarity.

Definition of self-similar in US English:

self-similar

adjective
Mathematics
  • (of an object or set of objects) similar to itself at a different time, or to a copy of itself on a different scale.

    〔数〕(物体,一组物体)自型的

    the result has the property of being self-similar, a magnified portion looks like the whole
    Example sentencesExamples
    • We would like to understand the projections of self-similar sets in the plane.
    • He noted that the body is full of fractals, self-similar repeating patterns at different scales, just as nature is full of fractals.
    • A fractal is a mathematical object that is self-similar irrespective of scale.
    • Since the creature does not change shape, rather simply grows larger, the most efficient way to do this is for its shell to grow in the self-similar form of a logarithmic spiral.
    • Indeed, nature features many irregular shapes that are self-similar - that repeat themselves on different scales within the same object.
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