Transmutation Mapping and Chromatic Notation: Building an intuition for apotheosis

[cursive summit]

Damn. Maybe I'm bad at explaining things concisely hehe

So the mood vector is basically the weighted average of the ingredients in the recipe. If you have a recipe of two items with the same energy and count, the mood vector will be exactly in the middle of the two items in the essence space.

[mellow citrus]

I’d love it it will show the item it will give using images

[lone canyon]

https://www.desmos.com/calculator/ef5snlibgv
made a representation of an item

[mellow citrus]

[lone canyon]

note this does include rank because i made it before i learned it does nothing

[wind relic]

ohhhh alpha channel right

[cursive summit]

The energy determines the weight an item has in that average; low energy relative to the other ingredients means the mood vector is further from it, high relative energy means the average is closer to it.

[lone canyon]

afaik tho alpha is always 1

[cursive summit]

I actually haven't double checked if alpha is used at all, so that could be true and it could be 16.

[lone canyon]

oh so mood vector is just the energy ratio(s)

[wind relic]

there is also the chance that I forgot the actual number of dimensions and my memory filled it in with 17 from ||the minimum distance you can get to Maria before she disappears||

[lone canyon]

afaik it isnt, given hzs site doesnt give item alpha and he's prob the 2nd most knowledgable on the topic, short only of lucy themselves

[cursive summit]

Kiiiiinda? The mood vector is a point in the essence space, but where it is is determined by the average location of the ingredients in essence space and weighted by their energy. The game then checks the distance from the mood vector to all the items, with that distance also being weighted by bias and tags, and then whichever item it's closest to is the output. The 'area/hypervolume of bias' is just the weighted area/hypervolume in which any point inside it is considered closest to the associated item.

[lone canyon]

are you calling the mood vector what i called my "perfect result"?

[cursive summit]

I think so, yes. In the game's code it's called the mood vector, which is why I call it that.

[lone canyon]

oh
weird
but for clarification-the mathematical result of apotheosis, which is what items are compared to to find cost of each one?

[cursive summit]

What do you mean by cost?

[cursive summit]

This is really cool, would you be ok if I maybe built something using this later?

[lone canyon]

basically the distance across all dimensions (and that dimensions weight)
like how tags are a full -1, while essences are + [the difference between mood vector's and the item's] and color is that weird formula hzs was talking about with square roots

[lone canyon]

i was thinking about making a second one which fuses into a third but each single point is a unique line of math with a variable (theres 40 something)

(oh yeah sure btw pop off queen)

[lone canyon]

ive mentioned it before, in my previous big explain cost is the actual sorting, its compressing a comparision of 2 16 ish dimensional points (mood vector and given potential product] into a single float

[cursive summit]

I... Think I understand? Are you calling the distance the cost? Like, the sorting is done by the distance from the mood vector to each of the items in the essence space, weighted by tags and bias. Are you calling that ranking by distance the ranking by cost?

[lone canyon]

product with the lowest cost wins (can and likely will be negative)

[cursive summit]

Ok, yes, you are calling the distance cost

[lone canyon]

thats what hzs calls it when he explains it so its what i use 🤷‍♂️

but yeah its basically distance

except it can go negative

[cursive summit]

Why don't we use the terminology used in the code, what

[lone canyon]

i assumed cost was what it was called

[cursive summit]

yeah, that's the reason why I didn't use add tags in my little 2D model

[lone canyon]

thats a question for hzs
he IS online

[cursive summit]

I would love to talk to him about this, but I might have to wait until later/tomorrow because I'm actually supposed to be writing a magazine review article that's due tomorrow >.<;;

Procrastination, yippeeeee

[unique urchin]

I'm just used to calling it cost because that is what it's usually called in the context of algorithms and optimization problems

[cursive summit]

Ohh, I see

[unique urchin]

Either that or it's called loss but calling it a "cost" just made more sense to me

I think the apotheosis algorithm ignores the A value. The color distance function only uses R, G, and B.

What I call cost is actually called distance in the code though, I just end up calling it cost whenever I'm not specifically trying to use the terminalogy in the code

like, to me, since it's the sum of multiple distances, tag match metrics, and penalties, it's not really a "distance"

but when talking about optimization problems it's pretty normal to call such a thing a "cost"

it just feels more natural to me

[lone canyon]

makes sense

[cursive summit]

another one

[fresh steppe]

Oh dang, that abble isn't strict hierarchy

I missed that somehow

[lone canyon]

good to see we’ve surpassed the actual tome

[cursive summit]

Hehe, I made it in the tome but just posted the png from the files here

rather than a screenshot

[mellow citrus]

Having a hard time mapping out, tooth block

[lone canyon]

chomp chomp

[cursive summit]

I mapped the letters. I don't know any recipes for the letter cube, but if I could I would try to include that in these, because the letter d is unfuseable.

[unique urchin]

I don't think a recipe for letter cube exists, the properties are really unfavorable

[cursive summit]

That's really unfortunate. I swear I saw someone with some in a cache cube in a stream a while back, I wonder if they modded it in...

[wind relic]

unfusable according to lucidpedia

[unique urchin]

It does have the fuseable tag in the game, it is just that there is no known recipe (and a recipe likely does not exist)

[wind relic]

ah

[lone canyon]

[lone canyon]

does he know
or is he a fake ball knower

[unique urchin]

I have a guess

[cursive summit]

I'm prototyping a new feature. I noticed that a lot of triplets have one of the members that produce more/less from the others (lower/higher relative energy), and so I've begun to add a chord line beside items that give more and a dot inside the triangle next to items that give less.

Currently the way I've been writing it have somewhat complex rules that result in minimal vagueness, but I'm considering if maybe I should simplify the rules at the cost of being a little more vague.

I'll see if I can write out the rules I've been trying out:

1. If any two of the triplet have have no product mults, they are seen as the baseline, and the third is either marked as multiplicative or divisive.
2. If the three are all unequal in relative energy/produce different amounts based on the combination of the others, the one that produces the most is marked as multiplicative, the one that produces the least is marked as divisive, and the third receives no marking.
3. If the triplet already contained a junk pair with product multipliers, those take priority in the notation. Triplet mults aren't notated on those two. Instead, if the third produces more than both, it's marked as multiplicative, if it produces less than both it's marked as divisive.

I find that this helps me with understanding the relative energy each item in a family has.

[cursive summit]

-# with every addition this notation becomes less approachable auau I am making my way to the title of Grand Alchemist... Grand Apotheologist?

[fresh steppe]

Mmmm this is real good

[cursive summit]

Alright, there has been a big addition to the site: Elemental Mutations. It is currently under a new Advanced Notation section, in which the contents assume a knowledge of the info panel and item elements.
https://paletteheart.nekoweb.org/chroma_note.html#advanced
As well as that, here are a couple maps that utilize this feature.

In those maps, it documents that the ball wand and foliage picker both may be made into a hate wand by raising their hate, and that a string may be made into a metal hook by raising its mercury.

I'm really happy with how it turned out, the table and vectors I made for it was an especially fun little touch to make.

I'm hoping tomorrow to get the new product multiplier marks for triplets into the guide.

[cursive summit]

Alright, the triplet multipliers have been added to the documentation. They're real useful for charting the energy difference between triplet members, as well as compressing notation.
https://paletteheart.nekoweb.org/chroma_note.html#mult-triplets

[fresh steppe]

Hell yeah

[cursive summit]

Lots of maps in the gallery have been updated with triplet multipliers, and the two maps I've made with elemental mutations have been added as well.