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Self-Similarity


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. 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 Hausdorff dimension.


See also

Fractal, Hausdorff Dimension

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References

Harris, J. W. and Stocker, H. "Scaling Invariance and Self-Similarity" and "Construction of Self-Similar Objects." §4.11.1-4.11.2 in Handbook of Mathematics and Computational Science. New York: Springer-Verlag, p. 113, 1998.Hutchinson, J. "Fractals and Self-Similarity." Indiana Univ. J. Math. 30, 713-747, 1981.

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Self-Similarity

Cite this as:

Weisstein, Eric W. "Self-Similarity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Self-Similarity.html

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