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[GIF] Advance (Morphing squares)

Posted 2 years ago
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Morphing squares

Advance

Just some recursive squares morphing into diamonds.

Source code:

midpoints[pts_] := Mean[{#, RotateLeft[#]} &[pts]];

smootherstep[x_] := 6 x^5 - 15 x^4 + 10 x^3;

DynamicModule[
 {cols = RGBColor /@ {"#2677bb", "#fbfbfb"}, 
  pts = 2 Sqrt[2] CirclePoints[4], t},
 Animate[
  t = smootherstep[Mod[s, 1]];
  Graphics[{
    Table[{FaceForm[
         If[OddQ[i] && s < 1 || EvenQ[i] && s >= 1, cols[[1]], cols[[2]]]], 
        Polygon[Riffle[#[[i]], (1 + t) midpoints[#[[i]]]]]}, {i, 1, Length[#]}] &@NestList[midpoints, pts, 30]},
   PlotRange -> {{-4/3*.99, 4/3*.99}, {-.99, .99}}, ImageSize -> {800, 600}],
  {s, 0, 2}]
 ]
4 Replies

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Nice! But it 'hurts' watching it morph, my brain can't handle it, not a good idea...

Sure. Just use CirclePoints[n] instead of CirclePoints[4] and make the appropriate modification to the scaling on midpoints[#[[i]]].

Plug in your preferred n in the following code and play around with depth until the center completely fills in:

midpoints[pts_] := Mean[{#, RotateLeft[#]} &[pts]];

smootherstep[x_] := 6 x^5 - 15 x^4 + 10 x^3;

DynamicModule[
 {n = 8, depth = 100, cols = RGBColor /@ {"#2677bb", "#fbfbfb"}, pts, t},
 pts = 2 Sqrt[2.] CirclePoints[n];
 Animate[
  t = smootherstep[Mod[s, 1]];
  Graphics[{
    Table[
       {FaceForm[If[OddQ[i] && s < 1 || EvenQ[i] && s >= 1, cols[[1]], cols[[2]]]], 
        Polygon[Riffle[#[[i]], (1 + t (Sec[π/n]^2 - 1)) midpoints[#[[i]]]]]},
       {i, 1, Length[#]}] &@NestList[midpoints, pts, depth]},
   PlotRange -> 1, ImageSize -> 540],
  {s, 0., 2}]
 ]

Here's what comes out for octagons:

Morphing nested octagons

Simple and elegant! Thanks for sharing! Can this be extended to n-gons? pentagon? hexagon?

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