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][1]


  [1]: https://i.stack.imgur.com/2fKvU.png