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My First 8x8 Ortho
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A little over a year ago I put away all of my notes concerning xor and orthos. Then, about 3 weeks ago, my brain started up again and wouldn't shut-up. I started working on it again and things just started exploding in my brain. A few days ago I had managed this: [code] 0 1 3 2 4 5 7 6 3 2 1 0 6 7 4 5 1 0 2 3 5 4 6 7 2 3 0 1 7 6 5 4 4 5 6 7 2 3 1 0 6 7 5 4 1 0 3 2 7 6 4 5 0 1 2 3 5 4 7 6 3 2 0 1 4 5 7 6 2 3 0 1 5 4 6 7 3 2 1 0 0 1 3 2 6 7 5 4 1 0 2 3 7 6 4 5 6 7 4 5 0 1 2 3 7 6 5 4 1 0 3 2 3 2 0 1 5 4 7 6 2 3 1 0 4 5 6 7 [/code] That is an 8x8 ortho that I had created in 4d space. Orthos are basically a single transversal in 4d space, so why not? Those do look an awlful lot like xor at a glance, but they are not. Let me perm/reduce one for ya real quick: [code] 0 1 2 3 4 5 6 7 1 0 3 2 5 4 7 6 2 3 0 1 7 6 4 5 3 2 1 0 6 7 5 4 4 5 6 7 1 0 2 3 5 4 7 6 0 1 3 2 6 7 5 4 3 2 0 1 7 6 4 5 2 3 1 0 [/code] A lot of it does look like xor, but it is broken in a few places. I didn't intend to break it just quite yet, but I did and I am *very* happy with it. That is absolutely gorgeous. I am doing it manually using Pygame. Playing a kind of board game in 4d on a 2d screen is interesting. Once I understand the rules a little better, it shouldn't take much to code it to where it will solve 100% of the time. And there is this really bizarre pattern in xor that I can't quite figure out. Most of it is easy to see, but there are anomolies that I can't explain. It's recursive or self-modifying or something. It is right on the tip of my brain and it drives me crazy. I'll be at my regular job and then start staring off into space trying to see what lies beneath. I can already flex pretty damn hard as it is, but once I see the underlying driving force, I will be unstoppable. I will get it, and I will shake the pillars of Heaven yet again. My work continues. Cheers.
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