2 added 461 characters in body
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As an alternative, you can also use Image3D to visualize 3-variable functions:

valueInterval = Through[{MinValue, MaxValue}[
    {x^2 + y^3 + z^4, And @@ Thread[-1 <= {x, y, z} <= 1]}, {x, y, z}]];

Outer[
    Function[{z, y, x}, If[x > 0 && y > 0 && z > 0, 0,
      4 Mod[Rescale[x^2 + y^3 + z^4, valueInterval], 1/5]
      ]], Reverse@#, Reverse@#, #] &@
  Range[-1, 1, .02] //
 Image3D[#, ColorFunction -> "RainbowOpacity",
   Boxed -> True, Axes -> True, AxesOrigin -> {1, 1, 1}/.02,
   AxesLabel -> (ToBoxes[Style[#, 20]] & /@ {x, y, z})] &

Image3D contoursImage3D contourplot

Or a 3D version DensityPlot:

Outer[
    Function[{z, y, x}, If[x > 0 && y > 0 && z > 0, 0,
      Rescale[x^2 + y^3 + z^4, valueInterval]^2.2
      ]], Reverse@#, Reverse@#, #] &@
  Range[-1, 1, .02] //
 Image3D[#, ColorFunction -> "RainbowOpacity",
   Boxed -> True, Axes -> True,
   AxesLabel -> (ToBoxes[Style[#, 20]] & /@ {x, y, z})] &

Image3D densityplot

As an alternative, you can also use Image3D to visualize 3-variable functions:

valueInterval = Through[{MinValue, MaxValue}[
    {x^2 + y^3 + z^4, And @@ Thread[-1 <= {x, y, z} <= 1]}, {x, y, z}]];

Outer[
    Function[{z, y, x}, If[x > 0 && y > 0 && z > 0, 0,
      4 Mod[Rescale[x^2 + y^3 + z^4, valueInterval], 1/5]
      ]], Reverse@#, Reverse@#, #] &@
  Range[-1, 1, .02] //
 Image3D[#, ColorFunction -> "RainbowOpacity",
   Boxed -> True, Axes -> True, AxesOrigin -> {1, 1, 1}/.02,
   AxesLabel -> (ToBoxes[Style[#, 20]] & /@ {x, y, z})] &

Image3D contours

As an alternative, you can also use Image3D to visualize 3-variable functions:

valueInterval = Through[{MinValue, MaxValue}[
    {x^2 + y^3 + z^4, And @@ Thread[-1 <= {x, y, z} <= 1]}, {x, y, z}]];

Outer[
    Function[{z, y, x}, If[x > 0 && y > 0 && z > 0, 0,
      4 Mod[Rescale[x^2 + y^3 + z^4, valueInterval], 1/5]
      ]], Reverse@#, Reverse@#, #] &@
  Range[-1, 1, .02] //
 Image3D[#, ColorFunction -> "RainbowOpacity",
   Boxed -> True, Axes -> True, AxesOrigin -> {1, 1, 1}/.02,
   AxesLabel -> (ToBoxes[Style[#, 20]] & /@ {x, y, z})] &

Image3D contourplot

Or a 3D version DensityPlot:

Outer[
    Function[{z, y, x}, If[x > 0 && y > 0 && z > 0, 0,
      Rescale[x^2 + y^3 + z^4, valueInterval]^2.2
      ]], Reverse@#, Reverse@#, #] &@
  Range[-1, 1, .02] //
 Image3D[#, ColorFunction -> "RainbowOpacity",
   Boxed -> True, Axes -> True,
   AxesLabel -> (ToBoxes[Style[#, 20]] & /@ {x, y, z})] &

Image3D densityplot

1
source | link

As an alternative, you can also use Image3D to visualize 3-variable functions:

valueInterval = Through[{MinValue, MaxValue}[
    {x^2 + y^3 + z^4, And @@ Thread[-1 <= {x, y, z} <= 1]}, {x, y, z}]];

Outer[
    Function[{z, y, x}, If[x > 0 && y > 0 && z > 0, 0,
      4 Mod[Rescale[x^2 + y^3 + z^4, valueInterval], 1/5]
      ]], Reverse@#, Reverse@#, #] &@
  Range[-1, 1, .02] //
 Image3D[#, ColorFunction -> "RainbowOpacity",
   Boxed -> True, Axes -> True, AxesOrigin -> {1, 1, 1}/.02,
   AxesLabel -> (ToBoxes[Style[#, 20]] & /@ {x, y, z})] &

Image3D contours