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Logarithm
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===Fractals=== [[File:Sierpinski dimension.svg|The Sierpinski triangle (at the right) is constructed by repeatedly replacing [[equilateral triangle]]s by three smaller ones.|thumb|alt=Parts of a triangle are removed in an iterated way.]] Logarithms occur in definitions of the [[fractal dimension|dimension]] of [[fractal]]s.<ref>{{Citation|last1=Helmberg|first1=Gilbert|title=Getting acquainted with fractals|publisher=Walter de Gruyter|series=De Gruyter Textbook|location=Berlin, New York|isbn=978-3-11-019092-2|year=2007}}</ref> Fractals are geometric objects that are self-similar in the sense that small parts reproduce, at least roughly, the entire global structure. The [[Sierpinski triangle]] (pictured) can be covered by three copies of itself, each having sides half the original length. This makes the [[Hausdorff dimension]] of this structure {{math|1=ln(3)/ln(2) β 1.58}}. Another logarithm-based notion of dimension is obtained by [[box-counting dimension|counting the number of boxes]] needed to cover the fractal in question.
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