View source for Self-similarity

In [[mathematics]], a '''self-similar''' [[Object (mathematics)|object]] is exactly or approximately [[Similarity (geometry)|similar]] to a part of itself (i.e. the whole has the same shape as one or more of the parts).

== Description ==

Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same [[statistical properties at many scales]].

== Fractals ==

Self-similarity is a typical property of [[Fractal|fractals]].

== Scale invariance

[[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.

== Characteristics ==

The non-trivial similarity evident in fractals is distinguished by their fine structure, or detail on arbitrarily small scales.

== Counterexample ==

As a counterexample, whereas any portion of a straight line may resemble the whole, further detail is not revealed.

== See also ==

* [[Chaos theory]]
* [[Fractal]]
* [[Mathematics]]
* [[Object (mathematics)]]
* [[Scale invariance]]
* [[Similarity (geometry)]]

== External links == 

* [https://en.wikipedia.org/wiki/Self-similarity Self-similarity] @ Wikipedia