gives the line segments representing the n^(th)-step Sierpiński curve.

Details and Options


open allclose all

Basic Examples  (2)

A 2D Sierpiński curve:

Lengths of the approximations to the Sierpiński curve:

The formula:

Visualize the Sierpiński curve in 2D with splines:

Scope  (6)

Curve Specification  (2)

A 2D Sierpiński curve:

The ^(th) approximation of the Sierpiński curve:

Curve Styling  (4)

Sierpiński curves with different thicknesses:

Thickness in scaled size:

Thickness in printer's points:

Dashed curves:

Colored curves:

Options  (1)

DataRange  (1)

DataRange allows you to specify the range of mesh coordinates to generate:

Specify a different range:

Applications  (4)

SierpinskiCurve is constructed recursively by transforming segments into curves linked together by lines:

Next iteration:

Visualize the Sierpiński curve in 2D:

With splines:

Build a polygon:

Apply a Sierpiński curve texture to a surface:

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:

Neat Examples  (1)

Traversal animations:

Wolfram Research (2017), SierpinskiCurve, Wolfram Language function,


Wolfram Research (2017), SierpinskiCurve, Wolfram Language function,


Wolfram Language. 2017. "SierpinskiCurve." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2017). SierpinskiCurve. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_sierpinskicurve, author="Wolfram Research", title="{SierpinskiCurve}", year="2017", howpublished="\url{}", note=[Accessed: 23-April-2024 ]}


@online{reference.wolfram_2024_sierpinskicurve, organization={Wolfram Research}, title={SierpinskiCurve}, year={2017}, url={}, note=[Accessed: 23-April-2024 ]}