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vidthekid β 7-Color Torus
Published: 2013-05-07 19:15:54 +0000 UTC; Views: 708; Favourites: 8; Downloads: 8
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Description
You may or may not have heard of the 4-Color Theorem. It says that, when coloring a map of any number of regions (on a flat sheet of paper or a globe), only four colors are required to satisfy the condition that each region is a different color from all its neighbors. The guy who proved this died like a week or two ago, by the way.Well, as it turns out, donuts are more tricky. They can require up to seven colors. So here's a torus whose surface is divided into seven regions, each a different color, and each touching every other region.
Texture created in TurboCAD Deluxe and Paint Shop Pro. Still frames rendered in POVRay for Windows. Animated GIF compiled with ImageMagick.
Some final comments:
- Any resemblance to the Google Chrome logo is entirely accidental.
- Ooh, shiny!
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Comments: 3
It looks a lot of the Google chrome stuff...cool
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knowing you, i'd expect you to write your own ray tracer for it 
very very interesting about the 7 colours, i didn't know that. it seems strange to me that it's 7, not say an even number, because the torus is just a plane with periodic boundaries.
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These days I don't have the time to write my own raytracer without a good reason. Actually, I don't think I've ever quite got around to writing one in the past. I've had a project in mind for quite a while for which I was going to write a raytracer, but I'm beginning to think that won't be necessary. I haven't tested POVRay's atmospheric scattering features yet, so time will tellβ¦
Regarding the 7 colors, I've known about that for a long time. It was in one of my high school math textbooks. I guess it isn't well-known because there are so few occasions to color regions on a toroidal topology.
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