How to generate a picture like this?

Needs["PolyhedronOperations`"]
poly = Geodesate[PolyhedronData["Dodecahedron", "Faces"], 4];

amplitude = 0.15;
twist = 4;
verts = poly[[1]];
faces = poly[[2]];
phases = RandomReal[2 Pi, Length[verts]];
newverts[t_] := 
  MapIndexed[{Sequence @@ (RotationMatrix[twist Last[#1]].Most[#1]), 
      Last[#1]} (1 + amplitude Sin[t + phases[[First@#2]]]) &, 
   verts];
newpoly[t_] := GraphicsComplex[newverts[t], faces];

duration = 1.5;
fps = 24;
frames = Most@
   Table[Graphics3D[{EdgeForm[], newpoly[t]}, 
     PlotRange -> Table[{-(1 + amplitude), (1 + amplitude)}, {3}], 
     ViewPoint -> Front, Background -> Black, Boxed -> False], {t, 0, 
     2 Pi, 2 Pi/(duration fps)}];
ListAnimate[frames, fps]

The next thing you need is global illumination, but Mathematica doesn't have that as far as I know.

This is a starter

dat = Table[x^2 + y^2 + z^2, {x, -1, 1, 0.125}, {y, -1, 1, 0.125}, {z, -1, 1,  0.125}];

plots = Table[
noise = RandomVariate[NormalDistribution[0, 0.05], Dimensions[dat]];
Do[noise[[All, All, i]] *= 2, {i, 2, Length[noise] - 1, 2}];
ListContourPlot3D[dat + noise, Contours -> 1/2, Mesh -> False, 
Boxed -> False, Axes -> False, ContourStyle -> White ], {25}];

Export["test.gif", plots]