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ArrayMesh
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ArrayMesh

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ArrayMesh[array]

generates a mesh region from an array of rank d in which each cell has a geometric dimension d and represents a nonzero value of the array.

Details and Options

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

A 1D array mesh:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-exym7r
Out[1]=1

A 2D array mesh:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-b1ikh5
Out[1]=1

A 3D array mesh:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-cvjwm5
Out[1]=1

Scope  (2)Survey of the scope of standard use cases

Create a 1D array mesh:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-hu0p9b
Out[1]=1

2D array mesh:

In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-fdvkfs
Out[2]=2

3D array mesh:

In[3]:=3
✖
https://wolfram.com/xid/0bim24j6-idkoss
Out[3]=3

ArrayMesh works on SparseArray:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-dai66c
Out[1]=1

Options  (14)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/0bim24j6-ewpnb1
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-c5e4q9
Out[2]=2

Specify a different range:

In[3]:=3
✖
https://wolfram.com/xid/0bim24j6-fl0z4t
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0bim24j6-cil14m
Out[4]=4

DataReversed  (1)

DataReversed allows you to reverse the order of rows:

In[1]:=1
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https://wolfram.com/xid/0bim24j6-cdijct
Out[1]=1

Reverse the order of rows:

In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-m2w17p
Out[2]=2

MeshCellHighlight  (2)

MeshCellHighlight allows you to specify highlighting for parts of an ArrayMesh:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-e2kcpr
Out[1]=1

Individual cells can be highlighted using their cell index:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-cwcidd
Out[1]=1

Or by the cell itself:

In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-2fki6
Out[2]=2

MeshCellLabel  (2)

MeshCellLabel can be used to label parts of an ArrayMesh:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-bl33rv
Out[1]=1

Individual cells can be labeled using their cell index:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-bort25
Out[1]=1

Or by the cell itself:

In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-be468t
Out[2]=2

MeshCellMarker  (1)

MeshCellMarker can be used to assign values to parts of an ArrayMesh:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-klxbw7
Out[1]=1

Use MeshCellLabel to show the markers:

In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-wi9ar
Out[2]=2

MeshCellShapeFunction  (2)

MeshCellShapeFunction can be used to assign values to parts of an ArrayMesh:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-cgbxok
Out[1]=1

Individual cells can be drawn using their cell index:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-eypeya
Out[1]=1

Or by the cell itself:

In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-f41ype
Out[2]=2

MeshCellStyle  (3)

MeshCellStyle allows you to specify styling for parts of an ArrayMesh:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-o7aweo
Out[1]=1

Individual cells can be highlighted using their cell index:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-ca7yws
Out[1]=1

Or by the cell itself:

In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-h8b5ha
Out[2]=2

Give explicit color directives to specify colors for individual cells:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-9msou
Out[1]=1

PlotTheme  (2)

Use a theme with grid lines and a legend:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-dyzyu8
Out[1]=1

Use a theme to draw a wireframe:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-nai1vm
Out[1]=1

Applications  (15)Sample problems that can be solved with this function

Cellular Automaton  (5)

A two-dimensional cellular automaton evolution:

In[1]:=1
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https://wolfram.com/xid/0bim24j6-it4j2t
Out[1]=1

Show a sequence of steps in the evolution of a 3D cellular automaton:

In[1]:=1
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https://wolfram.com/xid/0bim24j6-6xr0e
Out[1]=1

Use an outer-totalistic 2D cellular automaton to generate a maze-like pattern:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-fn1sgs
Out[1]=1

Show a "glider" in the Game of Life:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-k8x02a
In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-b5ttz4
In[3]:=3
✖
https://wolfram.com/xid/0bim24j6-cup90a
Out[3]=3

Patterns generated by a sequence of 2D nine-neighbor rules:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-dcf9kz
Out[1]=1

Mean cell values:

In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-kgemwq
Out[2]=2

Image  (2)

Convert a 2D image to a MeshRegion:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-ct2s9f

Cells and styles:

In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-grdd9m
In[3]:=3
✖
https://wolfram.com/xid/0bim24j6-gr290v

The mesh:

In[4]:=4
✖
https://wolfram.com/xid/0bim24j6-bmzie6
Out[4]=4

Convert a 3D image:

In[1]:=1
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https://wolfram.com/xid/0bim24j6-w1ntyx
Out[1]=1

Cells and styles:

In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-xjoigy
In[3]:=3
✖
https://wolfram.com/xid/0bim24j6-2x3v2p

The mesh:

In[4]:=4
✖
https://wolfram.com/xid/0bim24j6-d8v7v5
Out[4]=4

Pattern  (2)

Generate a simple 2D pattern:

In[1]:=1
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https://wolfram.com/xid/0bim24j6-r9gb0
Out[1]=1

3D pattern:

In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-lza55
Out[2]=2

More involved patterns:

In[3]:=3
✖
https://wolfram.com/xid/0bim24j6-n6n9b
Out[3]=3

Construct a Seidel mesh, i.e. a mesh region with tunnels going in every direction without crossing:

In[1]:=1
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https://wolfram.com/xid/0bim24j6-fegfn9
In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-f1mo4m
Out[2]=2

By converting to a boundary mesh and styling it, it becomes easier to comprehend:

In[3]:=3
✖
https://wolfram.com/xid/0bim24j6-c3j8tk
Out[3]=3

SubstitutionSystem  (4)

A 1D Cantor mesh:

In[1]:=1
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https://wolfram.com/xid/0bim24j6-iby5gu
Out[1]=1

Length of the Cantor set at each stage:

In[2]:=2
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https://wolfram.com/xid/0bim24j6-f5kb
Out[2]=2

The formula:

In[3]:=3
✖
https://wolfram.com/xid/0bim24j6-tho3p
Out[3]=3

Steps in constructing a Cantor set:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-l23yw9
Out[1]=1

Create an analogous 2D nested object:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-l71i2c
Out[1]=1

3D Menger sponge:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-j5nb7l
Out[1]=1

Game Design  (2)

Build a 2D chessboard:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-k87gt4
In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-jl6kjf
In[3]:=3
✖
https://wolfram.com/xid/0bim24j6-fvjc0z
In[4]:=4
✖
https://wolfram.com/xid/0bim24j6-go2mqx
Out[4]=4

3D chessboard:

In[5]:=5
✖
https://wolfram.com/xid/0bim24j6-bufnyf
In[6]:=6
✖
https://wolfram.com/xid/0bim24j6-bwswuo
In[7]:=7
✖
https://wolfram.com/xid/0bim24j6-ekga9k
In[8]:=8
✖
https://wolfram.com/xid/0bim24j6-ckeze1
Out[8]=8

Generate tetrominoes, shapes composed of four squares each:

In[1]:=1
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https://wolfram.com/xid/0bim24j6-9cl1r6
Out[1]=1

Color tetrominoes:

In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-3d7fq5
In[3]:=3
✖
https://wolfram.com/xid/0bim24j6-cfo3k6
Out[3]=3

Properties & Relations  (6)Properties of the function, and connections to other functions

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

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-ghy46g
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-gzo2mh
Out[2]=2

ArrayMesh consists of intervals in 1D:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-mnr925
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-z0dup
Out[2]=2

Rectangles in 2D:

In[3]:=3
✖
https://wolfram.com/xid/0bim24j6-cvwv09
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0bim24j6-gwk1z
Out[4]=4

Hexahedrons in 3D:

In[5]:=5
✖
https://wolfram.com/xid/0bim24j6-hb84fz
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0bim24j6-fnic5d
Out[6]=6

ArrayPlot can be used to generate a plot:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-ctgeq3
In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-dll4xj
Out[2]=2

Show plot:

In[3]:=3
✖
https://wolfram.com/xid/0bim24j6-bd5mmf
Out[3]=3

MatrixPlot can be used to generate a plot:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-brd4xy
In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-e7j86b
Out[2]=2

Show plot:

In[3]:=3
✖
https://wolfram.com/xid/0bim24j6-cdmshz
Out[3]=3

Find a boundary mesh region by using BoundaryMesh:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-bh438e
Out[1]=1

DataRange-> range is equivalent to using RescalingTransform[{...}, range]:

In[1]:=1
✖
https://wolfram.com/xid/0bim24j6-ld8c8x
Out[1]=1

Use RescalingTransform:

In[2]:=2
✖
https://wolfram.com/xid/0bim24j6-fnvf06
In[3]:=3
✖
https://wolfram.com/xid/0bim24j6-cu6dma
Out[3]=3
Wolfram Research (2016), ArrayMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/ArrayMesh.html.
✖
Wolfram Research (2016), ArrayMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/ArrayMesh.html.

Text

Wolfram Research (2016), ArrayMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/ArrayMesh.html.

✖
Wolfram Research (2016), ArrayMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/ArrayMesh.html.

CMS

Wolfram Language. 2016. "ArrayMesh." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ArrayMesh.html.

✖
Wolfram Language. 2016. "ArrayMesh." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ArrayMesh.html.

APA

Wolfram Language. (2016). ArrayMesh. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArrayMesh.html

✖
Wolfram Language. (2016). ArrayMesh. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArrayMesh.html

BibTeX

@misc{reference.wolfram_2025_arraymesh, author="Wolfram Research", title="{ArrayMesh}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/ArrayMesh.html}", note=[Accessed: 08-May-2025 ]}

✖
@misc{reference.wolfram_2025_arraymesh, author="Wolfram Research", title="{ArrayMesh}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/ArrayMesh.html}", note=[Accessed: 08-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_arraymesh, organization={Wolfram Research}, title={ArrayMesh}, year={2016}, url={https://reference.wolfram.com/language/ref/ArrayMesh.html}, note=[Accessed: 08-May-2025 ]}

✖
@online{reference.wolfram_2025_arraymesh, organization={Wolfram Research}, title={ArrayMesh}, year={2016}, url={https://reference.wolfram.com/language/ref/ArrayMesh.html}, note=[Accessed: 08-May-2025 ]}