# Function of surface roughness

How do I draw with Mathematica a function like this? I would use a series of circles and find the surface.

Thanks!

ParametricPlot3D[{r Cos[θ], r Sin[θ], .2 RandomReal[]}, {r, 1, 2}, {θ, 0, 2 π},
ColorFunction -> Function[y, Blend[{Red, Blue}, y]]]

ParametricPlot3D[{r Cos[θ], r Sin[θ], Sin[20 θ]/15},
{r, 1, 2}, {θ, 0, 2 π},
ColorFunction -> Function[{x, y, z, u}, Blend[{Red, Pink, LightBlue, Blue}, y]],
Mesh -> None, Boxed -> False, Axes -> False, PlotPoints -> 30,
Background -> Black] • Very nice, +1, but I think there should be a certain amount of randomness somewhere
– eldo
Dec 1, 2015 at 22:57

Just play with it, using functions with periods that divide 2 Pi:

ParametricPlot3D[{r Cos[θ], r Sin[θ],
0.015 (Sin[7 θ + 10 r Cos[2 θ]] + Sin[5 θ + 10 r Sin[2 θ]]) +
0.025 Sin[30 θ + Sin[θ]] + (r - 2)^2 Cos[3 θ + 0.73] - 0.15 r},
{r, 2, 3}, {θ, 0, 2 π},
Mesh -> None,
ColorFunction -> Function[{x, y, z, r, θ},
ColorData["ThermometerColors"][y]],
PlotPoints -> {15, 60}, PlotRangePadding -> {0, 0, 0.5},
Background -> Black, Boxed -> False, Axes -> False] (I mean, it's not like an anatomy lesson.)

• Nicely done. (+1) Dec 2, 2015 at 0:28