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Infinite Macaroni

Browsing /r/perfectloops I came across this fun animation:

Not only is it fun to watch, but you quickly start to wonder what it looks like on the inside after a few loops. It’s constantly being distended, so whatever the walls of this infinite macaroni are made of keep getting thinner. Does the cross section change? If so, what’s the pattern?

Let’s assume that when the animation starts, the macaroni ring we see is completely solid. When the animation has completed its first loop (heh), we’re left with another ring, but this time it’s hollow. The center of the ring has been drawn out into a tube and closed onto itself, leaving an open space. Kind-of like a pool noodle whose ends are made to touch.

With this image in our heads, let’s start the second loop of the animation. This one might be the trickiest to visualize, so bear with me. Keeping in mind the idea of a pool noodle with touching ends, pause the animation a few frames after it’s begun. What we have now is sort of like one of those water-tube-toys you could buy at the aquarium:

The only difference being that instead of being filled with a green fluid, our macaroni is filled with empty space. And as the animation completes, the ends of the water-tube-toy like shape merge, leaving the inside of the tube-toy disconnected from the outside! And now we’re left with two concentric hollow macaronis! A cross section would look like an O inside of an O.

So what happens with the next loop? Luckily, we’ve already worked out what happens when this animation runs for a hollow macaroni! It produces another hollow macaroni inside of itself… So each time this animation runs, we double the number of concentric Os.

Depending on how these concenctric macaronis distribute themselves, as the number of iterations tends towards infinity we’ll approach a completely solid macaroni again! What a loop.