Animated prime factorization diagrams

Ideas
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1

Szabolcs found a cool page with some JavaScript code that animates transitions between prime factorization diagrams. They can be pretty hypnotic. I volunteered to take a shot at a Mathematica implementation. The code is pretty short, and the transitions are pretty basic so you can expand on them however you want (add pauses between transitions, ease-in/ease-out to the keyframes, etc). The JavaScript code is about 5500 characters and the Mathematica code is about 600. The JavaScript version does allow rewinding and has a little text display in the corner, but even with those additions the Mathematica code would still be vastly shorter.

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DynamicModule[{shapes, t, n, next, keyframes}, 
 shapes[i_] := 
  Thread@{Table[
     ColorData["BlueGreenYellow"]@Rescale[a, {1, i}], {a, i}], 
    Disk /@ First@
      Fold[Module[{pts = #[[1]], r = #[[2]], 
          n = #2}, {Join @@ 
           Table[# + n r Through@{Cos, Sin}[a 2 Pi/n + Pi/2] & /@ 
             RotationTransform[a 2 Pi/n + If[n == 2, Pi/2, 0]]@
              pts, {a, n}], n r}] &, {{{0., 0.}}, 1}, 
       Join @@ ConstantArray @@@ FactorInteger@i]};
 t = 1;
 n = 1;
 next[] := 
  keyframes = 
   Thread[{Prepend[#, #[[1]]], #2} & @@ (shapes /@ {n, n + 1})];
 next[];
 Dynamic[If[(t += .02) >= n + 1, n++; next[]];
  Graphics[{Blend[{#[[1]], #2[[1]]}, t - n], 
      Disk[#[[2, 1]] + (t - n) (#2[[2, 1]] - #[[2, 1]])]} & @@@ 
    keyframes, PlotRange -> t*{{-2, 2}, {-2, 2}}, AspectRatio -> 1, 
   ImageSize -> 300]]]
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2

Very nice, Michael, this should be a great edition to Rosetta Code or Code Golf targeted towards language comparisons.

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3

It’s neat that powers of 3 produce Sierpinski-triangle-like patterns.

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