Geometric Allegory source code

allegory.nb

data = Module[{n = 512},
   Table[
    RandomFunction[
       TransformedProcess[(1 + x[t]) {Cos[t], Sin[t]},
        x \[Distributed] BrownianBridgeProcess[1/12, {2 π i/n, 0}, {2 π + 2 π i/n, 0}], t],
       {2 π i/n, 2 π + 2 π i/n, π/50}]["ValueList"][[1]],
    {i, 1, n}]
   ];

allegory = 
  With[{cols = RGBColor /@ {"#FAFAFA", "#1C1C1C"}, 
    means = Mean[Norm /@ #] & /@ data},
   ListLinePlot[
    Evaluate[data, InterpolationOrder -> 2, AspectRatio -> 1, 
     PlotRange -> {{-#, #}, {-#, #}} &[2.1], Axes -> None, 
     ImageSize -> 2048, Background -> cols[[2]],
     PlotStyle -> Table[
       Directive[ColorData["DeepSeaColors"][5/2 (means[[i]] - .8)], Thickness[.001]],
       {i, 1, Length[means]}]]]];

Export["allegory.png", allegory]