SierpinskiMesh
gives a mesh region representing the n-step Sierpiński triangle.
SierpinskiMesh[n,d]
gives the n-step Sierpiński sponge in dimension d.
Details and Options
![](Files/SierpinskiMesh.en/details_1.png)
- SierpinskiMesh is also known as Sierpiński triangle and Sierpiński sponge.
- SierpinskiMesh[n] is generated from a triangle by repeatedly removing the middle triangle of the subsequent cells. »
- SierpinskiMesh[n] is equivalent to SierpinskiMesh[n,2].
- SierpinskiMesh takes the same options as MeshRegion, with the following additions:
-
DataRange Automatic the range of mesh coordinates to generate
![](Files/SierpinskiMesh.en/Image_3.gif)
Examples
open allclose allBasic Examples (2)
Options (12)
DataRange (1)
DataRange allows you to specify the range of mesh coordinates to generate:
MeshCellHighlight (2)
MeshCellHighlight allows you to specify highlighting for parts of a SierpinskiMesh:
MeshCellLabel (2)
MeshCellLabel can be used to label parts of a SierpinskiMesh:
MeshCellMarker (1)
MeshCellMarker can be used to assign values to parts of a SierpinskiMesh:
Use MeshCellLabel to show the markers:
MeshCellShapeFunction (2)
MeshCellShapeFunction can be used to assign values to parts of a SierpinskiMesh:
MeshCellStyle (2)
MeshCellStyle allows you to specify styling for parts of a SierpinskiMesh:
Applications (1)
SierpinskiMesh is generated from a triangle by repeatedly removing the middle triangle of the cells:
Properties & Relations (5)
The output of SierpinskiMesh is always a full-dimensional MeshRegion:
SierpinskiMesh consists of triangles in 2D:
Find the volume of the Sierpiński mesh in 3D at each stage:
Find the boundary mesh region of SierpinskiMesh:
DataRangerange is equivalent to using RescalingTransform[{…},range]:
Use RescalingTransform:
Possible Issues (1)
SierpinskiMesh can be too large to generate:
![](Files/SierpinskiMesh.en/6.gif)
Text
Wolfram Research (2017), SierpinskiMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/SierpinskiMesh.html.
CMS
Wolfram Language. 2017. "SierpinskiMesh." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SierpinskiMesh.html.
APA
Wolfram Language. (2017). SierpinskiMesh. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SierpinskiMesh.html