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If you take a long strip of paper, fold it in half as many times as you can, and unfold it, it'll make an approximation of the fractal shape called the Heighway dragon.
If you take two fractions, say 1/2 and 1/3, and add the numerators and denominators, you get the mediant, in this case 2/5. I don't know much about the mediant, but it is linked to Ford circles in a way I don't really understand, and I'm told mediants give a startling way of approximating the value of continued fractions.
This is old news, and I kind of figured it was the case, but I never looked at the source code before.
And I was reminded that complex numbers are key to quantum mechanics, something I missed when I was writing about complex numbers a year or two ago.