# [GIF] Making Tracks (Deformations of a spherical curve)

Posted 3 years ago
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 Making TracksThe underlying curve here is the intersection of the quartic surface $(1-x^2)^2+(1-y^2)^2=(1-z^2)^2$ with the unit sphere. This surface comes up in an interesting way in a project I'm currently working and which I'll describe in more detail at some point; for now, here are ten Gaussian translates.Code: DynamicModule[{cols, rands, y}, SeedRandom[40]; cols = RGBColor /@ {"#B36458", "#353E55"}; rands = Table[RandomVariate[NormalDistribution[0, .05], 3], {10}]; Manipulate[ Graphics3D[{cols[[1]], Thickness[.005], Opacity[.5], Table[y = Haversine[Clip[π s, {0, π}]]; {2 (-1)^m Norm[rands[[m]]] + # & /@ cols[[1]], Line[Table[{Sqrt[(1 - y^2)/(1 + y^2)], y, y Sqrt[(1 - y^2)/(1 + y^2)]}*{i, j, k} + rands[[m]], {s, Max[0, t - 1], Min[t, 1], 1/50}]]}, {i, {-1, 1}}, {j, {-1, 1}}, {k, {-1, 1}}, {m, 1, 10}]}, Lighting -> "Neutral", PlotRange -> 1.2, Boxed -> False, Axes -> None, ViewAngle -> π/8, ImageSize -> 540, Background -> cols[[2]]], {t, 0, 2}] ]