page_title: Self-similarity
section_title: In nature
hierarchical_section_title: Self-similarity / Examples / In nature
caption_attribution_description: Romanesco
context_page_description: 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.
  A time developing phenomenon is said to exhibit self-similarity if the numerical value of certain observable quantity
  measured at different times are different but the corresponding dimensionless quantity at given value of remain invariant. It happens if the quantity exhibits dynamic scaling.
context_section_description: Self-similarity can be found in nature, as well. To the right is a mathematically generated, perfectly self-similar image of a fern, which bears a marked resemblance to natural ferns. Other plants, such as Romanesco broccoli, exhibit strong self-similarity.
caption: Close-up of a Romanesco broccoli.
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