Chain Theory (I Feel Like A Scientist)

from Artificial Soul by Lavair

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about

This song started when I showed my father a musical idea he didn't like, and asked "why not just start with a simple drum loop?" Thank you to Shye for discovering chain theory and how it applies to ayeheya puzzles, as well as giving me an extremely in-depth explanation of how it works so I could read it ver batim in this song. I'm sorry for saying every parentheses as "bracket" regardless of whether it opens or closes.

lyrics

Regardless on whether the grid has an even or odd amount of shaded cells
We can show the unshaded cells directly gained from the shadeds (before regarding connectivity) will always be an even total
It will be 4n - (n^2/4+ total grid penalties)/penalties applied to the perimeter only
Maths aside, important part is that this will always be even
Now lets calculate how much borders in the grid will be passed through

The total amount of borders passed through will be: total grid penalties*(total shadeds against a border -1)/4
Hmmm, how do we find the total of shadeds against a border though
This is actually known
Penalty shows us that it will always be: (total shadeds-total regions -2 +(2ceilR/2 * 2ceilC/2)+(R-1) +(C-1))+1

You may recognise the end of that equation there
We can now ram these equations up against each other and simplify it all
I'm no maths whiz so ill just spit out Agnomy's result

(total shadeds-total regions -2 +(2ceilR/2 * 2ceilC/2)+(R-1) +(C-1)/4n*n^2)+1 + total perimeter penalties *2
Aka "blah blah blah times 2"
So it's even
So what does this mean exactly?
It means we cant have a situation in the grid where we make a chain link (area where the dominos of located cells overlap) shaded
Because even though we may situationally be able to avoid a contradiction there
It will axiomatically lead to an impossibility later on somewhere, or would imply that the grid does not contain symmetric regions
When I read this, it kinda blew my mind

credits

from Artificial Soul, released March 5, 2021

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Lavair Seattle, Washington

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To Where Wings Rust
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Shye helped me out on Artificial Soul. I am forever grateful for her work. This particular album is actually one of the best albums I've heard in a long time. BEAUTIFUL experimental sound design! Lavair
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