SierpinskiMesh

SierpinskiMesh[n]

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

SierpinskiMesh[n,d]

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

Details and Options

Examples

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Basic Examples  (2)

A 2D Sierpiński mesh:

Areas of the approximations to the Sierpiński mesh:

A 3D Sierpiński mesh:

Scope  (3)

A 2D Sierpiński mesh:

A 3D Sierpiński mesh:

The ^(th) approximation of the Sierpiński mesh:

Options  (12)

DataRange  (1)

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

Specify a different range:

MeshCellHighlight  (2)

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

Individual cells can be highlighted using their cell index:

Or by the cell itself:

MeshCellLabel  (2)

MeshCellLabel can be used to label parts of a SierpinskiMesh:

Individual cells can be labeled using their cell index:

Or by the cell itself:

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:

Individual cells can be drawn using their cell index:

Or by the cell itself:

MeshCellStyle  (2)

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

Individual cells can be highlighted using their cell index:

Or by the cell itself:

PlotTheme  (2)

Use a theme with grid lines and a legend:

Use a theme to draw a wireframe:

Applications  (1)

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

In 3D:

Properties & Relations  (5)

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

SierpinskiMesh consists of triangles in 2D:

Tetrahedrons in 3D:

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:

Introduced in 2017
 (11.1)