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*[[教育空间]] ℝ<sup>''n''</sup> 有豪斯多夫维数 ''n''，循环'''S'''<sup>1</sup> 拥有豪斯多夫维数1.<ref name="schleicher" />
*[[教育空间]] ℝ<sup>''n''</sup> 有豪斯多夫维数 ''n''，循环'''S'''<sup>1</sup> 拥有豪斯多夫维数1.<ref name="schleicher" />
* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].<ref name="mandelbrot" /> For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3) ≈ 0.63.<ref>{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}</ref> The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of 1/2; this yields a Hausdorff dimension of ln(3)/ln(2) ≈ 1.58.<ref name=CampbellAnnenberg15/> These Hausdorff dimensions are related to the "critical exponent" of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].
* [[Fractal]]s often are spaces whose Hausdorff dimension strictly exceeds the [[topological dimension]].<ref name="mandelbrot" /> For example, the [[Cantor set]], a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3) ≈ 0.63.<ref>{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}</ref> The [[Sierpinski triangle]] is a union of three copies of itself, each copy shrunk by a factor of 1/2; this yields a Hausdorff dimension of ln(3)/ln(2) ≈ 1.58.<ref name=CampbellAnnenberg15/> These Hausdorff dimensions are related to the "critical exponent" of the [[Master theorem (analysis of algorithms)|Master theorem]] for solving [[Recurrence relation|recurrence relations]] in the [[analysis of algorithms]].
*[[分形]]一般是那些豪斯多夫维数直接超过其拓扑维数的空间。例如[[康托尔集]]是一个o维拓扑空间，由两个自己复制而成，每一个复制品都是原来的三分之一，因此它的豪斯多夫维数是 ln(2)/ln(3) ≈ 0.63。<ref>{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}</ref>一个[[谢尔宾斯基三角]]是他自身三个复制的组合。每一个是原来的 1/2，它的豪斯多夫维数ln(3)/ln(2) ≈ 1.58。<ref name=CampbellAnnenberg15/> 这些豪斯多夫维数
*[[分形]]一般是那些豪斯多夫维数直接超过其拓扑维数的空间。例如[[康托尔集]]是一个o维拓扑空间，由两个自己复制而成，每一个复制品都是原来的三分之一，因此它的豪斯多夫维数是 ln(2)/ln(3) ≈ 0.63。<ref>{{cite book | last=Falconer | first = Kenneth |title=Fractal Geometry: Mathematical Foundations and Applications | publisher=[[John Wiley and Sons]] | edition=2nd | year=2003}}</ref>一个[[谢尔宾斯基三角]]是他自身三个复制的组合。每一个是原来的 1/2，它的豪斯多夫维数ln(3)/ln(2) ≈ 1.58。<ref name=CampbellAnnenberg15/>在递归算法中解决递归关系时，这些豪斯多夫维数与[[算法分析主定理]]的临街指标相联系。
* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.
* [[Space-filling curve]]s like the [[Peano curve]] have the same Hausdorff dimension as the space they fill.
*[[空间填充曲线]]拥有和他们填充空间同样的豪斯多夫维数，如[[皮亚诺曲线]]。
*[[空间填充曲线]]拥有和他们填充空间同样的豪斯多夫维数，如[[皮亚诺曲线]]。