Puzzle Description:

A single surface object. The part in green is meant to show where the bottle passes through itself and is on the "inside". This is what you get if you fuse the edges of a mobius strip.

#1: Brian Bellis (mootpoint) on Aug 20, 2012 [SPOILER]

Check out http://www.kleinbottle.com/whats_a_klein_bottle.htm and then http://vimeo.com/20390916

After checking out the web sites, good representation on your part. It hurts my brain to think about things like this. Fractals hurt my brain too.

wow... above my head, Bran....but the solve was cool

I've seen those :)

For fractal amazingness (sorry about the headache, Norma), check out broccoli Romanesco:
http://www.wired.com/wiredscience/wp-content/gallery/fractal/fractal_10.jpg
Each nodule repeats the shape of the entire head of broccoli, and you can see at least 4 iterations in this photograph.

That is so cool Kristen.

Thanks for the web site. Totally intriguing.

I love it when math and art collide. I love fractals and 4th dimensions. Stuff like this is like a roller coaster for my brain. Wheeeeeee!

Super puzzle, Brian. The solve was great fun, and the image is fascinating.

Thank you.

Black was a little challenging but solved once I found the next step. Green required a little bit of line logic.

The clue is in C10: if R13-16 are filled, you end up with a group of one green in C11. This is impossible. I also used a twisted form of edge logic on the SQUARE clue in R19; if made to be a "4", then you have a group of three in the above row. Also wrong. This combination gave me enough to finish the puzzle.

SQUARE CLUE HINTS:
- The green squares in C7 include a 4.
- Every black square on the left is a 1.

An entire playlist about Klein Bottles, mostly featuring Cliff Stoll of Acme Klein Bottle fame. Well, "fame".
https://www.youtube.com/playlist?list=PLt5AfwLFPxWIpgtcFs_7fHGUedGEKu73p

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