spiral.nb

(* Code for _As Within, So Without_, which can be seen at https://shonk.tumblr.com/post/124422452191/ *)

Stereo[p_] := p[[;; -2]]/(1 - p[[-1]]);

Manipulate[
 ParametricPlot3D[
  Stereo[
   {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, Cos[t], -Sin[t]}, {0, 0, Sin[t], Cos[t]}}.
    {Sin[θ/24] Cos[θ], Sin[θ/24] Sin[θ], Cos[θ/24], 0}],
  {θ, -24 π, 0},
  PlotRange -> 20, 
  PlotStyle -> 
   Directive[CapForm["Round"], Thickness[.005], ColorData["Pastel"][1]], 
  Axes -> False, Background -> GrayLevel[.97], ImageSize -> 540, 
  Boxed -> False, ViewAngle -> π/120],
 {t, 0, 2 π}]