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[GIF] Stripes (Hyperbolic geodesics)

GROUPS:

Hyperbolic geodesics

Stripes

Another animation using the hyperbolic geodesic code explained in more detail here, inspired by this GIF on Tumblr.

In this case, I have two non-antipodal points on the unit circle and pairs of points traveling the two (unequal) arcs between them in the same amount of time, connected by hyperbolic geodesics in the Poincaré disk model (which are just circle arcs perpendicular to the unit circle).

Here's the code:

Stereo[{x_, y_, z_}] := {x/(1 + z), y/(1 + z)};
InverseStereo[{x_, y_}] := 1/(1 + x^2 + y^2) {2 x, 2 y, 1 - x^2 - y^2};
hypgeo[p1_, p2_, t_] := 
  Stereo[Append[#, 
      Sqrt[1 - Norm[#]^2]]] &[(1 - t) InverseStereo[p1][[;; 2]] + 
    t InverseStereo[p2][[;; 2]]];

DynamicModule[{cols = 
   RGBColor /@ {"#EDF2F6", "#FF5656", "#6A7EFC", "#494953"},
  n = 3,
  m = 72,
  pts,
  t
  },
 Manipulate[
    t = Mod[s, n/m];
    pts = 
     Table[{{Cos[2 π/n (t + a) + π/6], 
        Sin[2 π/n (t + a) + π/6]},
       {Cos[-2 (n - 1) π/n (t + a) + π/6], 
        Sin[-2 (n - 1) π/n (t + a) + π/6]}},
      {a, 0, 1 - n/m, n/m}];
    Show[
     ParametricPlot[
      Evaluate[hypgeo[#[[1]], #[[2]], r] & /@ pts], {r, 0, 1},
      PlotStyle -> (If[EvenQ[Floor[s/(n/m)]], #, 
           Reverse[#]] &[{Directive[cols[[3]], Thickness[.00275]], 
          Directive[cols[[2]], Thickness[.00275]]}]), Axes -> False],
     Graphics[{Thickness[.004], cols[[1]], Circle[], cols[[2]]}],
     Background -> cols[[-1]], PlotRange -> 1.2, ImageSize -> 540
     ],
    {s, 0., 2 n/m - #, #}] &[n/(24 m)]
 ]
POSTED BY: Clayton Shonkwiler
Answer
10 months ago

enter image description here - another post of yours has been selected for the Staff Picks group, congratulations! We are happy to see you at the top of the "Featured Contributor" board. Thank you for your wonderful contributions, and please keep them coming!

POSTED BY: Moderation Team
Answer
10 months ago

Group Abstract Group Abstract