Square Up

Just an animation of the graph of $f(x,y)=\frac{6}{5} \sin^3(\theta/2) \sin(6 \theta) \sin x \sin y$ as $\theta$ ranges from $0$ to $2\pi$.

Of course, originally this was just the surface with PlotStyle->None and with an appropriately-spaced mesh (which, as @J. M. has been pointing out to me in various threads, is much faster), but there doesn't seem to be a good way to get MeshStyle to color a single mesh line in different colors (something like ColorFunctions), so I had to build my own mesh with lines and color it with VertexColors.

Also, I'm experimenting with some different code formatting, so let me know if you have any strong opinions:

With[
 {
  n = 20,
  a = 1.2,
  k = 6,
  cols = RGBColor /@ {"#28C7FA", "#FF304F", "#002651"}
  },
 Manipulate[
  Graphics3D[
   {
    AbsoluteThickness[1.5],
    Table[
         Line[#[[i]], VertexColors -> (Blend[cols[[;; -2]], (# + a)/(2 a)] & /@ #[[i, ;; , 3]])],
         {i, Length[#]}] & /@ {#, Transpose[#]}
      &[Table[{2 ? (x - 1)/n, 2 ? (y - 1)/n, 
       a*Haversine[?]^(3/2) Sin[k ?] Sin[2 ? (x - 1)/n] Sin[2 ? (y - 1)/n]},
      {x, 1, n + 1}, {y, 1, n + 1}]
     ]
    },
   Boxed -> False,
   PlotRange -> {{-.5, 2 ? + .5}, {-.5, 2 ? + .5}, {-2.5, 2.5}},
   ImageSize -> 540,
   ViewPoint -> {2, 0, 1},
   SphericalRegion -> True,
   Background -> cols[[-1]]],
  {?, 0, 2 ?}]
 ]