self-similarity
Sign in to savethumb|right|250px|A Koch snowflake has an infinitely repeating self-similarity when it is magnified. thumb|300px|Standard (trivial) self-similarity
In the Vinony graph
Within Vinony's link graph, self-similarity is referenced by 256 other articles, and connects out to Sierpiński triangle, Cantor set and Sierpinski carpet.
It is catalogued under topics including Fractals, Homeomorphisms and Scaling symmetries.
Its subject is documented across 38 Wikipedia language editions.
Wikidata facts
- Subclass of
- similarity
- Image
- Feigenbaumzoom.gif
Show 4 more facts
- Commons category
- Self-similarity
- studied by
- category theory
- has characteristic
- scale invariance
- used by
- fractal
Sources (3)
via Wikidata · CC0
~5 min read
Encyclopedic overview
10 sectionsContents
- Self-affinity
- Definition
- Examples
- In cybernetics
- In nature
- In music
- See also
- References
- External links
- Self-affinity
thumb|right|250px|A Koch snowflake has an infinitely repeating self-similarity when it is magnified. thumb|300px|Standard (trivial) 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.
Excerpted from Wikipedia’s “self-similarity” article, available under the CC BY-SA 4.0 licence.