On Mixtures of the Four Elements in Seven Parts

[kleptoquark]

Here's something fun that might be useful for a fictional universe or something: I'm cataloging seven-part mixtures of the four classical elements. For example, this lil guy is one part Water, two parts Earth, three parts Fire, and one part Air:



We need to be systematic about this, so let's split the elements into "hot" (Fire and Air) and "cold" (Water and Earth). Here are all the mixtures that are either 100% cold (left) or 100% hot (right):



The right column is just the left column with each element swapped with its opposite (Fire/Water and Earth/Air).

If we have some nontrivial combination of cold and hot, like a 3:4 mix, we get something like this:



The left half is 4 parts hot to 3 parts cold, with Air gradually replacing Fire as you move right and Earth replacing Water as you move down. The right half (4 parts cold to 3 parts hot) is a copy of the left half with opposite elements swapped.

So we have a system! There are two other grids like this, for 1:6 and 2:5 mixes of hot and cold. Let's see what a full table of our elemental mixtures looks like:



hey wait a minute

Comments

[kleptoquark]

what do you mean, "that's too much effort for a shitpost"

[sigmaleph]

that's an entirely appropriate amount of effort for a shitpost and i appreciate it

[youzicha]

how did you discover this??

[kleptoquark]

:D :D :D

It actually started with some dude's observation that electron orbitals (neglecting spin) fit neatly into alternate layers of a tetrahedron. Recently it occurred to me that, hey, tetrahedra are the correct way to display mixtures of four things, just like ternary plots for three!

A little bit of fiddling later, here we are.

[etirabys]

Indignantly points out that earth should be hot

[kleptoquark]

You're gonna have to take that up with Aristotle, I'm afraid.