Vi Hart - Fractal Fractions

How to make snazzy-lookin' fractal equations using simple algebra.
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Around 4:30, If any number of layers of 2s equals 2 in that pattern, and you know that ultimately every result of 2 is a denominator with a numerator of 1, that's 1/2, and 1/2 + 1/2 = 1, and so no problem, right?

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