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  2. 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-similarity

    The self-similarity principle states that, when you make network contacts, you tend to choose people who resemble you in terms of experience, training, worldview, and so on.

    hbr.org/2005/12/how-to-build-your-network
     
  3. People also ask
    What is self-similarity in math?
    Self-similarity is the repetition of a shape, form or behavior on different levels of complexity. Not as an identical copy, but as a variation of the same basic shape. And how do mathematicians do it? An image that displays self-similarity is usually called a fractal.
    What is a self-similar object?
    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. [ 2]
    Why is self-similarity important?
    Self-similarity is a really big deal. It occurs all over nature and many have argued that self-similarity is one of the key natural principles that shape our world the way it is. Self-similarity has been observed in all fields of research: physics but also biology and even psychology and sociology.
    What is a self-similar phenomenon?
    A 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 can sometimes be described using heavy-tailed distributions, also known as long-tailed distributions.
    How do you define self-similar groups?
    There are many ways to define self-similar groups. One way is, as was just men- tioned, to define them as groups generated by Mealy type automata. This makes self-similar groups suitable for needs of computer science.
    What is the difference between scale invariance and self-similarity?
    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.
     
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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

    Examples image

    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 more

     
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