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Hey, Gilbert. I just wrote some stuff that takes this to a simpler level. Things have been crazy busy lately with RL. Here is the post that should shed some light: ----------- Since last post, my understanding has increased dramatically. Unfortunately, been working 60hrs weeks at my regular job and things have been progressing extremely slowly. Which is kind of a good thing because I am taking more time to mull things over and finding traps before I even think about code. That is, I'm finding logic bombs before they can become logic bombs. My first mistake was thinking in terms of swaps. Just like it sounds - take two things and swap them. Thinking in this way isn't exactly conducive. It kept leading to anomalies that I couldn't explain. So I started thinking in terms of invert. Instead of taking two things and swapping them, use XOR to invert them. When I shifted my thinking as such, things started to make sense. New kinds of patterns started showing up that I could explain. Next mistake. In a few places in my notes I have scrawled the phrase, "It's in the bits!" It is indeed in the bits, but I was looking at them wrong. I was looking at bits in a 1d sequence. More anomalies that baffled me. Luckily, I love re-arranging data and thinking in terms more like dimensions. So I started looking at the bits in 2d. Check it out: [code] . . . X . X X X . . . X . X X X X X X . X . . . . . . X . X X X . . . X . X X X X X X . X . . . . . . X . X X X . . . X . X X X X X X . X . . . . . . X . X X X . . . X . X X X X X X . X . . . . . . X . X X X . . . X . X X X . . . X . X X X X X X . X . . . X X X . X . . . X X X . X . . . X X X . X . . . . . . X . X X X . . . X . X X X . . . X . X X X . . . X . X X X . . . X . X X X X X X . X . . . X X X . X . . . X X X . X . . . X X X . X . . . X X X . X . . . X X X . X . . . X X X . X . . . X X X . X . . . [/code] Aren't those amazing? I love those little guys. They make it so easy to see what I've been missing. In each one of those squares, there are 4 X's in each row and column. I brute-force interated it and there are 2,450 of them. But the trick isn't just 4 X's in each row and column, but in their relationship to each other. There has to be a very specific relationship between them: they have to be "compatible". That compatibility takes the form of: [code] [0,0]=25% [0,1]=25% [1,0]=25% [1,1]=25% [/code] Once you have 6 of them that are compatible, you have orthogonal latin squares of size=8. If you find 8 that are compatible, you have MOLS=3 of size=8. And one of the cool things is that it doesn't matter what order you put them in when putting them together. Once you have one set of orthogonal latin squares, you can re-order the bit-planes and still have valid latin squares (and MOLS). As long as the 25% relationship remains intact, none of that other shit matters. I have done some reading about orthos and it was either Euler or Knuth that pointed to a structure that looks like this: [code] 0 1 0 1 1 0 3 2 [/code] I can now explain that using bit-planes and distribution. OMG, I haven't even touched on distribution. Thinking in terms of distribution is another thing that has really helped me figure things out. This goes back to the 25% thing. The 1d version is 50% and the 2d version is 25%. Basic bits and XOR sequence in 1d: [code] ....XXXX ..XX..XX .X.X.X.X [/code] Can you see it? Can you see how the 1d'ness of that leads to the 2d'ness of the above squares? Can you see how half are the same and half are different between any 2 lines of bits? Can you see how this leads to 25%? [code] ....XXXX ..XX..XX 50% = same 50% = different [..]=25% [X.]=25% [.X]=25% [XX]=25% ------------ ....XXXX .X.X.X.X 50% = same 50% = different [..]=25% [X.]=25% [.X]=25% [XX]=25% ------------ ..XX..XX .X.X.X.X 50% = same 50% = different [..]=25% [X.]=25% [.X]=25% [XX]=25% [/code] Yeah, it really is like that. Pretty wicked easy, yes? And that is the start of the underlying dynamics of all of this. Man, I love this stuff. [small](Edited by [url=https://ozoneasylum.com/user/351]warjournal[/url] on 08-16-2020 16:43)[/small]
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