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I have a list like

SeedRandom[1]
MatrixForm[list = RandomInteger[5, {5, 5}]]

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We can plot it with MatrixPlot directly with 2D style

MatrixPlot[list]

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I hope to plot it with 3D style.This is current method

Histogram3D[Catenate[Table @@@ Catenate[MapIndexed[{#2, #} &, list, {2}]]], 
 ColorFunction -> ColorData["Rainbow"]]

Mathematica graphics

But I don't know how to plot a matrix with real number.Such as

SeedRandom[1]
MatrixForm[list = RandomReal[5, {5, 5}]]

Is there any elegant method can do this?

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  • $\begingroup$ Something like a cityplot, then. How do you want negative or complex entries to be handled? $\endgroup$ – J. M.'s discontentment♦ Apr 25 '17 at 4:53
  • $\begingroup$ @J.M. Good link,and “For complex matrices the modulus (absolute value) of each element is displayed” as the description. $\endgroup$ – yode Apr 25 '17 at 5:09
  • $\begingroup$ This discussion might be of interest (or useful.) $\endgroup$ – Anton Antonov Apr 25 '17 at 13:21
  • $\begingroup$ @yode Why do you want to plot the matrix in 3D? Is it because the cell colors of MatrixPlot are not informative enough? $\endgroup$ – Anton Antonov Apr 25 '17 at 13:54
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    $\begingroup$ Isn't this a duplicate of Height-dependent filling color in 3D Data Plots? $\endgroup$ – István Zachar May 4 '17 at 17:53
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You can use ListPlot3D with InterpolationOrder -> 0:

ListPlot3D[list, InterpolationOrder -> 0, ColorFunction -> Hue, 
 Mesh -> None, Filling -> Axis]

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But unfortunately I've failed to find a way to color the block under each square accordingly with FillingStyle or with other means domestic to ListPlot3D.

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  • $\begingroup$ Fun,if you can make the color of those transparent pillar same to its top-face,I will accept this answer for its concise. $\endgroup$ – yode May 4 '17 at 16:53
  • $\begingroup$ @yode Yeah, now that is the hard part I hoped you won't ask for : ) $\endgroup$ – István Zachar May 4 '17 at 18:01
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    $\begingroup$ Thanks for the accept, but I should admit that coloring boxes according to top color seems impossible for ListPlot3D. $\endgroup$ – István Zachar May 4 '17 at 18:17
  • $\begingroup$ Yep,I have tried that just. But I like this solution still. :) $\endgroup$ – yode May 4 '17 at 18:30
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Graphics primitives is quite elegant:

box[h_, {x_, y_}] := Cuboid[{x, y, 0}, {x + 1, y + 1, h}]
Graphics3D@MapIndexed[box, list, {2}]

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It is no less elegant with custom styling:

box[h_, {x_, y_}] := {
  ColorData["Rainbow", h/Max[list]],
  Cuboid[{x, y, 0}, {x + 1, y + 1, h}]
  }
Graphics3D@MapIndexed[box, list, {2}]

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Here's an example with the color function that is used by MatrixPlot, see J.M.'s comment below:

Mathematica graphics

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  • 2
    $\begingroup$ If MatrixPlot[]'s coloring is desired, here is the necessary color function. $\endgroup$ – J. M.'s discontentment♦ Apr 25 '17 at 6:23
  • $\begingroup$ @J.M. Nice, especially because of the way it was found out. Thank you for sharing. $\endgroup$ – C. E. Apr 25 '17 at 15:26
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Also:

SeedRandom[1]
list = RandomReal[5, {5, 5}];

BarChart3D:

BarChart3D[Reverse /@ list, ChartLayout -> "Grid", 
   BarSpacing -> {0, 0}, ColorFunction -> "Rainbow", 
   "Canvas" -> False, "FaceGrids" -> None][[1]] // 
 Graphics3D[#, Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}] &

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DiscretePlot3D:

iF = Interpolation[Join @@ MapIndexed[Composition[Reverse, List], list, {2}]];

DiscretePlot3D[iF[i, j], {i, 1, Dimensions[list][[1]]}, {j, 1, Dimensions[list][[2]]}, 
 ExtentSize -> Full, FillingStyle -> Opacity[1], ColorFunction -> "Rainbow"]

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ListPlot3D:

Normal[ListPlot3D[list, InterpolationOrder -> 0, ColorFunction -> Hue, Mesh -> None]] /. 
 {Line[__] :> Sequence[], Polygon[x : {__},  VertexColors -> {col_, ___}, ___] :>  
 {col, EdgeForm[], Opacity[.9], Cuboid @@ ({{1, 1, 0}, 1} Sort[x][[{1, -1}]])}}

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Here is a plot based on this answer of "Plotting “Terrain” with “Water” on them Using BarChart3D"

{n, m} = Dimensions[list];
{cx, cy} = {1/4, 1/4};
Graphics3D[{Red, Opacity[0.1], 
  Cuboid[{1/2, 1/2, 0}, {n + 1/2, m + 1/2, 0}], 
  Table[Tooltip[{Red, Opacity[0.1], 
     Cuboid[{i, j, 0}, {i + cx, j + cy, list[[i, j]]}], Blue, 
     Opacity[0.3], 
     Cuboid[{i, j, list[[i, j]]}, {i + cx, j + cy, list[[i, j]]}]}, 
    BarChart[list[[i]], PlotLabel -> Row[{"row:", i}], 
     ChartLayout -> "Stacked"]], {i, n}, {j, m}]}, Axes -> True, 
 Boxed -> False, BoxRatios -> {n/Max[n, m], m/Max[n, m], 1/3}, 
 ImageSize -> Large]

enter image description here

The idea is to make the plot more informative by (1) making the bars to be thinner and more transparent, and (2) providing a tooltip showing a 2D BarChart with stacked layout for each row.

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