WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home Page »

SierpinskiMesh

✖

gives a mesh region representing the n^(th)-step Sierpiński triangle.

✖

gives the n^(th)-step Sierpiński sponge in dimension d.

Details and Options

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

A 2D Sierpiński mesh:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-iby5gu
Out[1]=1

Areas of the approximations to the Sierpiński mesh:

In[2]:=2
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-f0ufzu
Out[2]=2

A 3D Sierpiński mesh:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-h6u9e7
Out[1]=1

Scope  (3)Survey of the scope of standard use cases

A 2D Sierpiński mesh:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-fdvkfs
Out[1]=1

A 3D Sierpiński mesh:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-idkoss
Out[1]=1

The ^(th) approximation of the Sierpiński mesh:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-dan8zd
Out[1]=1

Options  (12)Common values & functionality for each option

DataRange  (1)

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

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-ewpnb1
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-c5e4q9
Out[2]=2

Specify a different range:

In[3]:=3
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-fl0z4t
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-cil14m
Out[4]=4

MeshCellHighlight  (2)

MeshCellHighlight allows you to specify highlighting for parts of a SierpinskiMesh:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-gbljzi
Out[1]=1

Individual cells can be highlighted using their cell index:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-de38c0
Out[1]=1

Or by the cell itself:

In[2]:=2
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-fxydv9
Out[2]=2

MeshCellLabel  (2)

MeshCellLabel can be used to label parts of a SierpinskiMesh:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-bl33rv
Out[1]=1

Individual cells can be labeled using their cell index:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-bort25
Out[1]=1

Or by the cell itself:

In[2]:=2
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-be468t
Out[2]=2

MeshCellMarker  (1)

MeshCellMarker can be used to assign values to parts of a SierpinskiMesh:

In[7]:=7
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-klxbw7
Out[7]=7

Use MeshCellLabel to show the markers:

In[8]:=8
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-wi9ar
Out[8]=8

MeshCellShapeFunction  (2)

MeshCellShapeFunction can be used to assign values to parts of a SierpinskiMesh:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-breuv8
Out[1]=1

Individual cells can be drawn using their cell index:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-mw7gs4
Out[1]=1

Or by the cell itself:

In[2]:=2
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-f41ype
Out[2]=2

MeshCellStyle  (2)

MeshCellStyle allows you to specify styling for parts of a SierpinskiMesh:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-o7aweo
Out[1]=1

Individual cells can be highlighted using their cell index:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-ca7yws
Out[1]=1

Or by the cell itself:

In[2]:=2
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-h8b5ha
Out[2]=2

PlotTheme  (2)

Use a theme with grid lines and a legend:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-dyzyu8
Out[1]=1

Use a theme to draw a wireframe:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-nai1vm
Out[1]=1

Applications  (1)Sample problems that can be solved with this function

SierpinskiMesh is generated from a triangle by repeatedly removing the middle triangle of the cells:

In[3]:=3
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-rvdhi
Out[3]=3

In 3D:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-12xkzg
Out[1]=1

Properties & Relations  (5)Properties of the function, and connections to other functions

The output of SierpinskiMesh is always a full-dimensional MeshRegion:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-ghy46g
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-gzo2mh
Out[2]=2

SierpinskiMesh consists of triangles in 2D:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-cvwv09
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-gwk1z
Out[2]=2

Tetrahedrons in 3D:

In[3]:=3
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-hb84fz
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-fnic5d
Out[4]=4

Find the volume of the Sierpiński mesh in 3D at each stage:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-eq7cn0
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-bpi11n
Out[2]=2

Find the boundary mesh region of SierpinskiMesh:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-nk00k
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-hxrdsa
Out[2]=2

DataRangerange is equivalent to using RescalingTransform[{…},range]:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-ld8c8x
Out[1]=1

Use RescalingTransform:

In[2]:=2
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-fnvf06
In[3]:=3
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-cu6dma
Out[3]=3

Possible Issues  (1)Common pitfalls and unexpected behavior

SierpinskiMesh can be too large to generate:

In[1]:=1
✖
https://wolfram.com/xid/0d4h9ljuyi5u9mty-tihoda
Out[1]=1
Wolfram Research (2017), SierpinskiMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/SierpinskiMesh.html.
✖
Wolfram Research (2017), SierpinskiMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/SierpinskiMesh.html.

Text

Wolfram Research (2017), SierpinskiMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/SierpinskiMesh.html.

✖
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.

✖
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

✖
Wolfram Language. (2017). SierpinskiMesh. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SierpinskiMesh.html

BibTeX

@misc{reference.wolfram_2025_sierpinskimesh, author="Wolfram Research", title="{SierpinskiMesh}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/SierpinskiMesh.html}", note=[Accessed: 29-March-2025 ]}

✖
@misc{reference.wolfram_2025_sierpinskimesh, author="Wolfram Research", title="{SierpinskiMesh}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/SierpinskiMesh.html}", note=[Accessed: 29-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_sierpinskimesh, organization={Wolfram Research}, title={SierpinskiMesh}, year={2017}, url={https://reference.wolfram.com/language/ref/SierpinskiMesh.html}, note=[Accessed: 29-March-2025 ]}

✖
@online{reference.wolfram_2025_sierpinskimesh, organization={Wolfram Research}, title={SierpinskiMesh}, year={2017}, url={https://reference.wolfram.com/language/ref/SierpinskiMesh.html}, note=[Accessed: 29-March-2025 ]}