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ArrayPlot3D—Wolfram Language Documentation

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• See Also
  • ArrayPlot
  • Image3D
  • ListDensityPlot3D
  • MatrixPlot
  • ReliefPlot
  • ComplexArrayPlot
  • DensityPlot3D
  • Raster3D
  • ListPlot3D
  • SparseArray
  • CellularAutomaton
  • ArrayMesh
  • Cuboid
• Related Guides
  • Data Visualization

ArrayPlot3D[array]

generates a plot in which the values in an array are shown in a discrete array of cubes.

• ArrayPlot3D[array] by default arranges the array elements a_ijk with increasing values of i going from top to bottom, j from back to front and k from left to right.
• Possible forms of array include:
• {{{a₁₁₁,…,a_11t},…,{a_1s1,…,a_1st}},…,{{a_r11,…,a_r1t},…,{a_rs1,…,a_rst}}} normal array SparseArray values as a normal array QuantityArray magnitudes NumericArray values as a normal array SymmetrizedArray values as a normal array Dataset values as a normal array
• If array is ragged, shorter dimensions are treated as padded on the right with empty space.
• If array contains 0s and 1s, the 1s will appear as black cubes and the 0s as empty space.
• ArrayPlot3D has the same options as Graphics3D, with the following additions and changes: [List of all options]
• The rules given by ColorRules are applied to the value a_ijk of each cell. The rules can involve patterns.
• If none of the rules in ColorRules apply, then ColorFunction is used to determine the color.
• With the default setting ColorRules->Automatic, an explicit setting ColorFunction->f is used instead of ColorRules.
• If the color determined for a particular cell is None, the cell is treated as empty space.
• If no color is determined for a particular cell, the cell is rendered in the color given by MissingStyle, by default a dark red color.
• ColorFunction and OpacityFunction are supplied with a single argument, given by default by the value of a_ijk scaled to be between 0 and 1.
• With DataReversed->True, the order of rows is reversed, so that rows run from bottom to top, with the last row at the top.
• With the setting TicksAutomatic, ticks are placed at round integers, typically multiples of 5 or 10.
• With the setting TicksAll, ticks are also placed at the minimum and maximum values of i, j and k.
• In explicit Ticks specifications, the tick coordinates are taken to refer to i, j and k.
• PlotRange can take the following forms:
• a_max show a_ijk values between 0 and a_max {a_min,a_max} show a_ijk values between a_min and a_max {range_i,range_j,range_k} show a_ijk values with i in range_i, … {range_i,range_j,range_k,range_a} show a_ijk values with i in range_i, … and a_ijk in range_a
• The array index ranges range_i, range_j and range_k can take the following forms:
• {min,max} include indices between min and max All include all indices
• Typical settings for PlotLegends include:
• None no legend Automatic automatically determine legend Placed[lspec,…] specify placement for legend
• Possible settings for Mesh include:
• Automatic automatically show the mesh None do not show the mesh Full show mesh adjacent to filled array cells All show mesh adjacent to all array cells {spec_i,spec_j,spec_k} show the mesh in particular dimensions
• The possible settings for Method include "Graphics3D", "Raster3D" and "ArrayMesh".

Plot an array of numbers:

Display the state of a 3D cellular automaton:

Specify overall color rules:

Use a standard blend as a color function:

By default, 0 is not plotted and 1 is plotted in black:

With no opacity, 0 is plotted in white:

Plot data with units:

Plot a ragged array, padding on the right:

Cells with value None are rendered like the background:

Plot a sparse array:

Make all cells cubes:

Use a different aspect ratio:

By default, ArrayPlot3D does not show any axes:

No axis labels are drawn by default:

Place a label on the axis:

Specify axes labels:

Change the style for the axes:

Specify the style of each axis:

Use different styles for the ticks and the axes:

Use different styles for the labels and the axes:

The default is to not show values outside the plot range:

Show values outside the plot range in red:

Show low values in gray and high values in green:

Map values from 0 to 1 onto colors according to Hue:

Use a pure function as the color function:

Use a named color gradient from ColorData:

Show elements with value 1 as black and all others as white:

Specify color rules for explicit values or patterns:

ColorFunction is used if no color rules apply:

Implement a "default color" by adding a rule for _:

Use any patterns in ColorRules:

Rules are used in the order given:

By default, array values are assumed to have integer i, j and k values:

Specify the i, j, k coordinate range for tabular data:

Reverse the order of j and k values:

Reverse the order of i, j and k values:

Insert mesh lines between all cells:

Default mesh style:

Make the mesh pink:

OpacityFunction is Automatic by default:

Use None to make the whole array opaque:

Use a custom opacity function to specify the opacity for each value:

Use a constant opacity Opacity[0.5]:

Plot all elements:

Plot only elements with values up to 3, leaving the rest empty:

The first three entries in PlotRange specify the range of i, j and k values to include:

Plot positive elements only:

Use a theme with detailed ticks and a legend:

Put ticks at round numbers:

Ticks at specific values:

Plot the state of a 3D cellular automaton:

Plot the evolution of a 2D three-color cellular automaton:

Highlight a specific element in an array:

Highlight a column of values:

Highlight a slice of an array:

Highlight a sub-block of values:

Plot the Sin function at integer points:

Evolution of a totalistic 3D cellular automaton:

Interactively map GCD values onto colors using Hue:

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