Two-Color Drawings

Start with a line.

IMG_01731Then add another line.

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And another, and another, and another, and keep going, until you’ve found something.

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It’s someone turning away from you, with sloppy wet hair and an umbrella. Don’t see it yet? Then pick a segment and color it. This character is feeling blue (it is, after all, raining, but she doesn’t know that yet), so start with blue.

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Now on every vertex of that segment (every place where it comes to a sharp point that border on another section), go and color that bordering section blue, too.

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Ah. It’s growing. Keep going.

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See the sphere? How’d that get there? And why has this worked every time so far? Why don’t we ever get two sections bordering each other of the same color?

. . .  Let’s keep going.

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It’s colored itself, with no mistakes. How? The secret is that there were no intersections where more than two lines intersected. As long as that’s true in the initial drawing, this always works – it’s been mathematically proven. And it magically always seems to produce incredibly cool and expressive pictures, but perhaps that’s more a testament to the human imagination. Art and math, working together. Huh.

Wait, didn’t I say she was holding an umbrella? Of course! It becomes much clearer once the coloring is finished. She may be feeling blue, but she also has some hope; the rain makes her happy. So she’ll also be green.

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Still don’t see the rain?

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