SierpinskiCurve
gives the line segments representing the n-step Sierpiński curve.
Details and Options
![](Files/SierpinskiCurve.en/details_1.png)
- SierpinskiCurve is also known as Sierpiński space-filling curve.
- SierpinskiCurve returns a Line primitive corresponding to a closed path around {0,0}.
- SierpinskiCurve takes a DataRange option that can be used to specify the range the coordinates should be assumed to occupy.
![](Files/SierpinskiCurve.en/Image_2.gif)
Examples
open allclose allBasic Examples (2)
Scope (6)
Options (1)
DataRange (1)
DataRange allows you to specify the range of mesh coordinates to generate:
Applications (4)
SierpinskiCurve is constructed recursively by transforming segments into curves linked together by lines:
Properties & Relations (3)
SierpinskiCurve consists of lines:
Find the perimeter of the 2D Sierpiński curve:
DataRangerange is equivalent to using RescalingTransform[{…},range]:
Use RescalingTransform:
Possible Issues (2)
By default, the coordinates of the Sierpiński curve are not in the unit square:
Using DataRange to generate the Sierpiński curve in the unit square:
SierpinskiCurve can be too large to generate:
![](Files/SierpinskiCurve.en/5.gif)
![](Files/SierpinskiCurve.en/6.gif)
Text
Wolfram Research (2017), SierpinskiCurve, Wolfram Language function, https://reference.wolfram.com/language/ref/SierpinskiCurve.html.
CMS
Wolfram Language. 2017. "SierpinskiCurve." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SierpinskiCurve.html.
APA
Wolfram Language. (2017). SierpinskiCurve. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SierpinskiCurve.html