For no reason, here's a quick primer on Homestuck troll relationships
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So, Homestuck introduces a species of alien trolls from a planet called Alternia. Rather than having only the form of romance represented by a heart (♥), trolls divide romance into four different quadrants, each represented by a suit of cards. I thought I'd provide a quick guide to how they work!
Troll romantic relationships are divided between red romance (redrom), which concerns positive emotions, and black romance (blackrom), which concerns negative emotions. They are further subdivided into the concupiscent (meaning "sexy") quadrants, which concern the trolls' idiosyncratic reproductive system, and the conciliatory quadrants, which are equivalent to what humans consider platonic, though they involve placating someone's violent tendencies, or preventing someone or someones from violently getting out of control (or any other kind of getting out of hand, really). Individually, they are referred to as the flushed, caliginous, pale, and ashen quadrants, named after their respective colors. When you are in a relationship with someone else in a particular quadrant, the quadrant is said to be "filled" for you.
Note that the troll reproductive system technically requires genetic material from two individuals per concupiscent pairing ("without going into too much detail!" as the narration hurriedly exclaims),1 but it does not require that they be of the opposite sex. They don't even have words for homosexuality or heterosexuality. (This is quite similar to the behavior of human shippers.) For this reason, the pronouns used in the examples are randomized every time you load the page.
The Four Quadrants
The Flushed Quadrant (♥)
matespritship: "he is her matesprit", "they are matesprits" (concupiscent, red)
This is romantic love as humans understand it. Nothing new here.
Etymology: A portmanteau of "mate" and "esprit" (French for "soul").
Examples: Alice and Marisa. :D Or, uh, Han Solo and Princess Leia was the first example which came to mind that actually exists in their canon. Wesley and Buttercup.
The Caliginous Quadrant (♠)
kismesissitude: "he is his kismesis", "they are kismeses" (concupiscent, black)
Romantic "hate" — that is, a relationship which has all the trappings of a romantic one, except that it is based on mutual hatred rather than mutual love. Two people in a caliginous relationship are "enemies" the way romantic lovers are "friends"; for instance, their behavior towards each other can be extremely vitriolic and hostile, and most of their interactions might be arguments and shouting matches ... but you just want to tell them, "Oh just get a room, you two."
Note that this is not the same as mortal enmity; kismeses want the relationship to continue, much as lovers/matesprits do (albeit for different reasons), and they certainly do not want to kill each other; at one point, a troll explains to a human that his kismesis "hates me, but not enough to kill me." However, it is quite possible for such a relationship to escalate to the point that the former kismeses do in fact want to kill each other. The reverse is also possible.
Late in Homestuck, a troll describes the feelings associated with kismesissitude to a human who seems to be experiencing them: It almost never involves full-blown antipathy, and rarely reaches that level of animosity in the long term; someone might have frustrated, negative feelings for her kismesis, or she might spend all of her time going out of her way to aggravate her, but these negative emotions don't comprehensively account for how they feel about each other. They actually do like/admire some things about each other — all healthy relationships must have some measure of respect — but the negatives make it difficult to articulate what the positives actually are, and in the end the positives only serve to accentuate or emphasize the negatives, i.e. "I'd really like her if it wasn't for everything I hate about her!" The human's reaction to this in-story summary is variations on "No no no!" but the troll reassuringly says that the "No no no!" is all part of the experience; it's supposed to feel messed up when you realize how you're feeling.
Hate dates, hatesnogging, and hatesex are optional, and all three are respectively mentioned, shown, and implied in Homestuck (notwithstanding the fact that sex works differently for trolls, "without going into too much detail"). Immense disappointment may occur if someone wants to fight you not because she hates you "that way," but because she believes that defeating you is the right thing to do.
Etymology: "kismet" (fate) plus "nemesis," stated before troll romance was introduced.
Examples You Could Interpret That Way: Any superhero/archvillain pair, when you think about it. Mara Jade initially has this one-sidedly for Luke Skywalker; a more two-way example would be Palpatine and Darth Vader, until the end (as it generally is with any Sith Master/Apprentice relationship). Calvin has either Susie Derkins (who was good at directly matching wits with him, and whom he went up against more often) or his babysitter Rosalyn (the only person he actually feared, and who was also good at directly matching wits with him).
The Pale Quadrant (♦)
moirallegiance: "she is her moirail", "they are moirails" (conciliatory, red)
Often misinterpreted as "best buds forever" or "heterosexual life partners"2 or "bromance" (regardless of their actual genders), but with the Homestuck trolls, the emphasis is on the fact that one or both of the two has particularly violent tendencies, even by troll standards, and their interactions with their moirail help to make them less dangerous to themselves and others. The relationship itself can take any number of forms, ranging from "she directly has a calming effect on her when they interract" to "she is really good at guilt-tripping her into not acting on the violent urges/desires." In any case, it's all about bringing out the best in your moirail.
This relationship obviously seems like it can be "one-way" (i.e. one of them is explicitly the dangerous one, while the other one is the designated moirail, who is not as dangerous); however, there are examples in Homestuck of a moirallegiance going both ways, with two characters serving to calm each other down at different points.
Etymology: "Moira" (the Greek personifications of fate) plus "allegience."
Examples You Could Interpret That Way: Arthur and The Tick. Chewbacca and Han Solo. Hayate Yagami and the entirety of the Wolkenritter.
The Ashen Quadrant (♣)
auspisticism: "she is their auspistice", "they are auspistices", "she will auspisticize for them" (conciliatory, black)
Basically, an auspistice mediates between two normal enemies (as opposed to kismeses), in order to prevent it from becoming too violent. For Homestuck trolls in particular, this also serves to help prevent "black infidelity" (i.e. if one or both of the two already has a kismesis).
Etymology: "auspicious" plus "armistice."
Examples You Could Interpret That Way: Kramer occasionally for Seinfeld and Newman. Emperor Palpatine for Luke Skywalker and Darth Vader, by accident. Nanako Dojima for Persona 4's Protagonist and Ryotaro Dojima.
Other Troll-Specific Notes
It is mentioned that, troll emotions being what they are, there is a possibility that a relationship might change quadrants. It's quite possible for a concupiscent relationship to flip between its red and black quadrants (this is referred to as "quadrant vacillation"); it's easier to go from love to hate than from apathy to either one, after all. There can also be problems if an auspistice, who has a certain amount of power over the other two, has different goals from the couple (i.e. if she has redrom feelings for one of them). Then there's the possibility of moirallegiance developing into matespritship (or kismesissitude, depending on the nature of the moirallegiance) ...
That said, you cannot have more than one relationship with the same individual simultaneously; or at any rate, you shouldn't. This is especially true for auspisticism, since this would result in a fairly blatant conflict of romantic interest.
Promiscuity is frowned upon no matter what quadrant we're talking about; at one point, a character is called a "village two wheel device" for trying to "auspisticize any two brinesuckers who sneer at each other" even though auspisticism doesn't even remotely resemble the original meaning of "village bicycle" (although to be fair, the character delivering the insult is a gigantic tool).
Trolls have a caste system, based on the color of their blood (the "hemospectrum," through all the colors of the rainbow, with the colors more drab at the bottom), which also affects their lifespan: drab-red and rust brown are at the bottom and have the shortest lifespan, yellow and green are middling, and blue (natch) and violet are at the top. Barring mutations, there are twelve different colors. When trolls write or type text (i.e. a journal or in instant-messaging), they tend to render it in the color of their blood, unless they have some sort of reason not to; this tendency is called "hemotyping." Caste does not seem to have any direct effect on relationship-prospects; in Homestuck, trolls have relationships of all varieties with any and all other members of the hemospectrum, i.e. a troll with indigo blood lusts after a red-blooded troll, who had previously been in a relationship with a yellow-blood.
Trolls reach puberty at approximately the same rate as humans. They measure their ages in "Alternian solar sweeps," and six solar sweeps is equivalent to thirteen Earth years. So one solar sweep is equivalent to 2 1/6 earth years (612 backwards, for those of you to whom this means anything). And two solar sweeps is equal to 4 1/3 years.
When you have not one, but four types of romance, you have effectively quadrupled your relationshipping-power!3 I mean, everybody ships Team Fortress 2's Heavy ♥ Medic, and Red Spy ♥ Blue Scout's Mother is canon. Why not Engineer ♠ Spy? You could also say that Pyro ♣ Spy/Sniper, using fire; this is, after all, the ashen quadrant.
"But," you say, "isn't the hatred rather one-sided on the Engineer's part? And what of settings which have no characters for which auspisticism or moirallegiance would make sense?" To which I say: when has that ever mattered to shippers!? I mean, look at me: I have depicted Kaguya and Mokou, who want to kill each other in canon, in a redrom relationship, to the extent that I dislike seeing either of them in any other redrom relationships!
The point is that there's no reason you can't say "Nitori ♣ Momiji/Hina," the same way there's no reason you can't say "Vetinari ♥ Lu Tze." (There's certainly plenty of stories which seem to have "Keine ♦ Mokou" when they don't have "Keine ♥ Mokou.") This simply offers new types of relationships. The possibilities are even more endless than they were before, and what you're doing is technically still shipping!
1In fact, no detail is given at all, aside from the fact that 1. each pairing must put their genetic material in a "filial pail" with either a heart or a spade symbol on it, to be collected by an imperial drone and brought to the Mother Grub, 2. a character states (well, ineptly denies) taking "a romantic hot air balloon ride suspended in a filial pail" with someone else, and 3. trolls therefore view buckets as being sexually explicit in and of themselves, and "filling a bucket" is naughty; of course, this might also have other connotations, since it is also stated that an Imperial Drone would kill a troll if they didn't both consupiscent quadrants filled, and none of the twelve trolls had both of them filled at the beginning of their story.
2i.e. "they're as close as it's possible for two people of the same gender to be, but there's nothing gay between them or anything."
3Actually, it's technically 4.25 times normal shipping, since auspisticism involves three people instead of two.
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Dizzy H. Slightly Voided
Partly, but I wouldn't leave it at that. The dynamic is obviously different for trolls who are more a danger to themselves than to others (like Equius), for one thing.
Also, it isn't necessarily morality-based; if you interpret Gamzee and Karkat's relationship at the beginning of Hivebent as a moirallegience, then it's quite clear that Gamzee is acting as the target for Karkat's RAGE, instead of particularly mitigating it.