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ArrayPlot3D

ArrayPlot3D[array]

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

Details and Options

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]

Axes	False	whether to draw axes
Boxed	True	whether to draw the bounding box
ClippingStyle	None	how to show cells whose values are clipped
ColorFunction	Automatic	how each cell should be colored
ColorFunctionScaling	True	whether to scale the argument to ColorFunction
ColorRules	Automatic	rules for determining colors from values
DataRange	All	the range of and values to assume
DataReversed	False	whether to reverse the order of rows
Lighting	"Neutral"	whether to use lighting
Mesh	Automatic	whether to draw a mesh
MeshStyle	Automatic	the style to use for a mesh
Method	Automatic	the method to use for displaying the array
MissingStyle	Automatic	the style to use for missing values
OpacityFunction	Automatic	how to compute the opacity at each cell
OpacityFunctionScaling	True	whether to scale the arguments to OpacityFunction
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotLegends	None	legends for datasets
PlotRange	All	the range of values to plot
PlotTheme	$PlotTheme	overall theme for the plot
TargetUnits	Automatic	units to display in the plot

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".

List of all options

AlignmentPoint	Center	the default point in the graphic to align with
AspectRatio	Automatic	ratio of height to width
Axes	False	whether to draw axes
AxesEdge	Automatic	on which edges to put axes
AxesLabel	None	axes labels
AxesOrigin	Automatic	where axes should cross
AxesStyle	{}	graphics directives to specify the style for axes
Background	None	background color for the plot
BaselinePosition	Automatic	how to align with a surrounding text baseline
BaseStyle	{}	base style specifications for the graphic
Boxed	True	whether to draw the bounding box
BoxRatios	Automatic	bounding 3D box ratios
BoxStyle	{}	style specifications for the box
ClippingStyle	None	how to show cells whose values are clipped
ClipPlanes	None	clipping planes
ClipPlanesStyle	Automatic	style specifications for clipping planes
ColorFunction	Automatic	how each cell should be colored
ColorFunctionScaling	True	whether to scale the argument to ColorFunction
ColorRules	Automatic	rules for determining colors from values
ContentSelectable	Automatic	whether to allow contents to be selected
ControllerLinking	False	when to link to external rotation controllers
ControllerPath	Automatic	what external controllers to try to use
DataRange	All	the range of and values to assume
DataReversed	False	whether to reverse the order of rows
Epilog	{}	2D graphics primitives to be rendered after the main plot
FaceGrids	None	grid lines to draw on the bounding box
FaceGridsStyle	{}	style specifications for face grids
FormatType	TraditionalForm	default format type for text
ImageMargins	0.	the margins to leave around the graphic
ImagePadding	All	what extra padding to allow for labels, etc.
ImageSize	Automatic	absolute size at which to render the graphic
LabelStyle	{}	style specifications for labels
Lighting	"Neutral"	whether to use lighting
Mesh	Automatic	whether to draw a mesh
MeshStyle	Automatic	the style to use for a mesh
Method	Automatic	the method to use for displaying the array
MissingStyle	Automatic	the style to use for missing values
OpacityFunction	Automatic	how to compute the opacity at each cell
OpacityFunctionScaling	True	whether to scale the arguments to OpacityFunction
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotLabel	None	a label for the plot
PlotLegends	None	legends for datasets
PlotRange	All	the range of values to plot
PlotRangePadding	Automatic	how much to pad the range of values
PlotRegion	Automatic	final display region to be filled
PlotTheme	$PlotTheme	overall theme for the plot
PreserveImageOptions	Automatic	whether to preserve image options when displaying new versions of the same graphic
Prolog	{}	2D graphics primitives to be rendered before the main plot
RotationAction	"Fit"	how to render after interactive rotation
SphericalRegion	Automatic	whether to make the circumscribing sphere fit in the final display area
TargetUnits	Automatic	units to display in the plot
Ticks	Automatic	specification for ticks
TicksStyle	{}	style specification for ticks
TouchscreenAutoZoom	False	whether to zoom to fullscreen when activated on a touchscreen
ViewAngle	Automatic	angle of the field of view
ViewCenter	Automatic	point to display at the center
ViewMatrix	Automatic	explicit transformation matrix
ViewPoint	{1.3,-2.4,2.}	viewing position
ViewProjection	Automatic	projection method for rendering objects distant from the viewer
ViewRange	All	range of viewing distances to include
ViewVector	Automatic	position and direction of a simulated camera
ViewVertical	{0,0,1}	direction to make vertical

Examples

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Basic Examples (4)

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:

Scope (6)

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:

Options (32)

AspectRatio (2)

Make all cells cubes:

Use a different aspect ratio:

By default, ArrayPlot3D does not show any axes:

AxesLabel (3)

No axis labels are drawn by default:

Place a label on the axis:

Specify axes labels:

AxesStyle (4)

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:

ClippingStyle (1)

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:

ColorFunction (2)

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:

ColorFunctionScaling (1)

With ColorFunctionScaling->True, the values are first scaled to lie between 0 and 1:

ColorRules (1)

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:

DataRange (1)

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

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

DataReversed (1)

Reverse the order of j and k values:

Reverse the order of i, j and k values:

Mesh (1)

Insert mesh lines between all cells:

MeshStyle (1)

Default mesh style:

Make the mesh pink:

OpacityFunction (4)

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]:

OpacityFunctionScaling (2)

By default, scaled values are used:

Use unscaled values by setting OpacityFunctionScaling to False:

PlotLegends (2)

No legend is used by default:

Generate a legend automatically:

PlotLegends automatically picks up ColorFunction:

PlotRange (2)

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:

PlotTheme (1)

Use a theme with detailed ticks and a legend:

Ticks (2)

Put ticks at round numbers:

Ticks at specific values:

Applications (6)

Cellular Automata (2)

Plot the state of a 3D cellular automaton:

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

Array Structures (4)

Highlight a specific element in an array:

Highlight a column of values:

Highlight a slice of an array:

Highlight a sub-block of values:

Properties & Relations (6)

Use ArrayPlot or MatrixPlot for 2D arrays:

ArrayPlot3D uses 3D arrays, even if one of the dimensions is 1:

Raster3D arranges elements in the opposite orders from ArrayPlot3D:

The DataReversed option allows ArrayPlot3D to use the same order as Raster3D:

Use ListDensityPlot3D for continuous densities, using varying opacity to see interior features:

Image3D uses interpolated volumetric rendering to display the data:

ReliefPlot creates artificial shadows for 2D data:

Use ComplexArrayPlot for 2D arrays of complex-valued data:

Neat Examples (3)

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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