[Undertale]
SWAP AU
Import/Export Matrix
About
Original sprite from Undertale, with new ones by Radnos.
Any suggestions? Send them to @radnos on Discord.
Don't count on me to respond until the summer holidays, but I'll definitely read them!
This started with me thinking about how, when you combine swapping and shifting, it behaves like multiplying matrices...
I then created a Python script to play with that idea.
And there I was, literally multiplying swap and shift AUs together, making a few discoveries along the way.
For example, did you know that if you apply Storyshift five times (Storyshift to the power of 5), you get a swap AU similar to what an Underswap AU take would give you? You can try it for yourself! Swap AUs have a symetric matrix, so the website will display it on the header if your AU is a swap one or not.
The same applies to Storyspin. Also, the matrix for Storyspin is the transpose of Storyshift, but it's also its inverse. Logical, right? Storyshift applied to Storyspin gives you Undertale, so multiplying their matrices returns the identity matrix, which is Undertale. So, Storyshift is a self-adjoint endomorphism... I wonder if every shift (of one loop) behaves like that? Probably.
Additionally, every shift AU, when raised to the power of half the number of characters in the shift loop, can become a swap AU... at least, from my testing? I don't have a rigorous mathematical proof. I found it pretty neat, though—it makes sense when you see it. What struck me was that Storyshift to the power of 10 gives back Undertale, which is interesting because each AU passed through its transformations until it returned to its original form.
I also think it's quite funny to apply this math vocabulary to Undertale AUs! ShiftPowerFive... multiplying Altertale and Underswap...
That is to say, I created this website to provide a more practical way of exploring this idea. For people who know a bit of algebra, the "base", a set of vectors created from each character's name, was arranged in a specific order so that Underswap would be the "upside-down" matrix of Undertale, which is the identity matrix. You can see this if you export Underswap as a matrix.
Hope you have fun! Playing with it really gives you ideas for original shifts and swaps you could create! I'll be on my way creating my Underflips or whatever...