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How can I choose the PlotStyle such that the four surfaces are visible (at least to some extent) in the following plot

 Plot3D[{Sin[0.5 x y], Cos[0.5 x y], Sin[x y], Cos[x y]}, {x, 0, 
  2 \[Pi]}, {y, 0, 2 \[Pi]}]

Edit: To be specific, I want these plots should look different from each other when one takes a black and white printout.

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    $\begingroup$ What exactly are you asking? All surfaces are visible when I run your command. $\endgroup$
    – Natas
    Jul 15, 2020 at 12:49
  • $\begingroup$ Maybe add some transparency? PlotStyle -> Opacity[.4] $\endgroup$
    – flinty
    Jul 15, 2020 at 12:59
  • $\begingroup$ @Natas, I mean when someone takes a black n white printout of this plot, he/she should be able to make the distinction in the surfaces to some extent. $\endgroup$
    – Rob
    Jul 15, 2020 at 13:08

2 Answers 2

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(* 12.1 *)
styles = {{Gray}, {HalftoneShading[], 
    White}, {HatchShading[.5], White}, {StippleShading[.3], White}};
Plot3D[{Sin[0.5 x y], Cos[0.5 x y], Sin[x y], Cos[x y]}, {x, 0, 
  2 π}, {y, 0, 2 π}, PlotStyle -> styles, Mesh -> None, 
 Lighting -> "Accent", PlotPoints -> 50]

enter image description here

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From the comments you seem to want a grayscale visible colorscheme. There are plenty of them, in Mathematica, check the documentation to ColorData. Also check the viridis colormap in mathematica: Colormaps for linear visual perception AND grayscale printing

With the colorscheme "AvocadoColors" you can get something like this:

color = ColorData["AvocadoColors"][#] & /@ Subdivide[0.2, 1, 3];
p = Plot3D[{Sin[0.5 x y], Cos[0.5 x y], Sin[x y], Cos[x y]}, {x, 0, 
   2 \[Pi]}, {y, 0, 2 \[Pi]}, PlotStyle -> color]
ColorConvert[p, "Grayscale"]

enter image description here

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  • $\begingroup$ Thanks, @Mr Puh, it would be nice if one can have these curves with different mesh styles, so that in black-n-white mode, one can actually differentiate these surfaces easily. Something like this: one surface with mesh lines, one with mesh dashed lines, one with mesh dotted lines, and one without mesh. $\endgroup$
    – Rob
    Jul 16, 2020 at 16:49
  • $\begingroup$ Use the option MeshStyle of Plot3D. $\endgroup$
    – Mr Puh
    Jul 16, 2020 at 17:54

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