Editing Scale invariance (section)

===Fractals===
[[File:Kochsim.gif|thumb|right|250px|A [[Koch curve]] is [[self-similar]].]]
It is sometimes said that [[fractal]]s are scale-invariant, although more precisely, one should say that they are [[self-similar]]. A fractal is equal to itself typically for only a discrete set of values {{mvar|λ}}, and even then a translation and rotation may have to be applied to match the fractal up to itself.

Thus, for example, the [[Koch curve]] scales with {{math|∆ {{=}} 1}}, but the scaling holds only for values of {{math|''λ'' {{=}} 1/3<sup>''n''</sup>}} for integer {{mvar|n}}. In addition, the Koch curve scales not only at the origin, but, in a certain sense, "everywhere": miniature copies of itself can be found all along the curve.

Some fractals may have multiple scaling factors at play at once; such scaling is studied with [[multi-fractal analysis]].

Periodic [[External ray|external and internal rays]] are invariant curves .