As usual great stuff!
While it is not fun to write for everyone I knew I need to try to optimize it. To my surprise I was able to make it smooth and completely FE side which means you can use it e.g. as a progress indicator:
\[CapitalPsi][m_, n_, {x_, y_}] := Sin[m \[Pi] x] Sin[n \[Pi] y];
DynamicModule[
{n = 20, a = 1.2, dots,
cols = RGBColor /@ {"#0098d8", "#f54123", "#0b3536"}, \[Theta],
colorGrid, cf},
dots = Table[{(*we can pregenerate the table and leave z coordinate \
'dynamic'*)
2 \[Pi] (x - 1)/n,
2 \[Pi] (y - 1)/n,
Cos[Dynamic[
2 Pi \[Theta]]] ((*we are preparing 'dynamic placeholder' to \
be used later. the rescaling to 0-2Pi done here can be done FE side.*)
1./Sqrt[2] \[CapitalPsi][3, 1, {(x - 1)/n, (y - 1)/n}] +
1/Sqrt[2] \[CapitalPsi][1, 3, {(x - 1)/n, (y - 1)/n}]
)
}, {x, 1, n + 1}, {y, 1, n + 1}];
Overlay[{
Animator[ Dynamic[\[Theta]], AppearanceElements -> None,
AnimationRate -> 1],
Graphics3D[{
AbsoluteThickness[2],
Table[With[{i = i},
Line[#[[i]], VertexColors -> (
Function[dynH,
RGBColor[(*'manual blend' because FE can handle basic \
arithmetic and not Blend itself. InputForm/@RGBColor/@{"#0098d8",
"#f54123","#0b3536"} *)
0.9607843137254902 (dynH + a)/(2. a),
0.596078431372549 + (0.2549019607843137 -
0.596078431372549) (dynH + a)/(2. a),
0.8470588235294118 + (0.13725490196078433 -
0.8470588235294118) (dynH + a)/(2. a)
],
Listable
]@#[[i, ;; , 3]]
)]
],
{i, Length[#]}
] & /@ {dots, Transpose[dots]}
},
Boxed -> False,
PlotRange -> {{0, 2 \[Pi]}, {0, 2 \[Pi]}, {-2, 2}},
ImageSize -> 540, ViewPoint -> {2, 0, 1/2},
SphericalRegion -> True, Background -> cols[[-1]]]
}, All, 2],
Initialization :> (\[Theta] = 0)
]
