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CantorMesh—Wolfram Language Documentation

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• See Also
  • CantorStaircase
  • SierpinskiMesh
  • ArrayMesh
  • MeshRegion
  • BoundaryMeshRegion
  • KaryTree
• Related Guides
  • Mesh-Based Geometric Regions
  • Iterated Maps & Fractals

CantorMesh[n]

gives a mesh region representing the n-step Cantor set.

CantorMesh[n,d]

gives the n-step Cantor set in dimension d.

A 1D Cantor mesh:

Lengths of the approximations to the Cantor mesh:

The formula:

A 2D Cantor mesh:

A 3D Cantor mesh:

A 1D Cantor mesh:

A 2D Cantor mesh:

A 3D Cantor mesh:

The approximation to the Cantor set:

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

Specify a different range:

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

Individual cells can be highlighted using their cell index:

Or by the cell itself:

MeshCellLabel can be used to label parts of a CantorMesh:

Individual cells can be labeled using their cell index:

Or by the cell itself:

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

Individual cells can be highlighted using their cell index:

Or by the cell itself:

Give explicit color directives to specify colors for individual cells:

Use a theme with grid lines and a legend:

Use a theme to draw a wireframe:

The Cantor set is generated from the unit interval by repeatedly removing the middle third of the cells:

In 2D:

In 3D:

Find the length of the Cantor mesh:

The general formula:

Find the measure of the 2D Cantor mesh:

The general formula:

Find the measure of the 3D Cantor mesh:

The general formula:

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