If you want to turn banality into beauty, start here with three staid and static squares:

Stage #1

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Now replace each red and yellow square with two new red and yellow squares orientated in the same way to the original square:

Stage #2

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And repeat:

Stage #3

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Stage #4

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Stage #5

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Stage #6

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Stage #7

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Stage #8

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Stage #9

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Stage #10

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Stage #11

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Stage #12

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Stage #13

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Stage #14

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Stage #15

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Stage #16

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Stage #17

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Stage #18

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And you arrive in the end at a fractal called a dragon curve:

Dragon curve

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Dragon curve (animated)

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Elsewhere other-engageable

• Curvous Energy — an introduction to dragon curves
• All Posts — about dragon curves