Sharingan Lore

10. Hereditary Mangekyou Sharingan

Officially, it is unclear if anything determines the pattern of a Mangekyou Sharingan. But from what little we know of the Sharingan, a case can be made that one's Mangekyou pattern is somewhat genetic and will resemble the Mangekyou of one's parent. For example, Fugaku and Itachi's Mangekyou Sharingan have a similar swirl pattern.

Of course, one could challenge that assumption by noting that Sasuke doesn't have a similar swirl pattern like his father or brother. Though I think the answer for that should be obvious: Sasuke is Indra's reincarnation, and Indra's reincarnation are an exception to the rule, since Madara alludes to him and Sasuke sharing a "straight tomoe" pattern, giving him and Sasuke something in common beyond blood. This is an allusion to him and Sasuke both being Indra's reincarnates, so apparently Sasuke's and Madara's patterns both have a similarity that gives that connection away.

Plus if one takes note that Sasuke's Mangekyou pattern is the exact same as Indra's Mangekyou pattern (in the anime version, anyway) it's obvious that Sasuke's Mangekyou is special and doesn't follow the typical rules, because as the reincarnation of an ancient being, Sasuke has as Sharingan patterning that follows a different standard.

But for the Uchiha who are not Indra's reincarnations, Fugaku and Itachi have similarities in their Mangekyou's patterning, as both have a swirled pattern. And Sarada's Mangekyou Sharingan looks loosely like an inversion of her father's pattern.

I assume that Mangekyou Sharingan abilities are hereditary as well, since Sasuke and Itachi are blood brothers and both of them happen to share the same Mangekyou ability Amaterasu. Although this is only pure conjecture and headcanon, I suspect that they inherited this Mangekyou ability from their father Fugaku, since I think there's a likely chance that Fugaku possessed the Amaterasu ability. For this reason, it seems like a possiblity that Sarada could have the Amaterasu ability as well.

I don't find it likely that Sasuke and Itachi are the only Uchiha who happen to share the same Mangekyou ability. I suspect that Kotoamatsukami is a Mangekyou ability that has been running through Shisui's bloodline for some time, since despite being so young, Shisui is very informed about the duration of time it takes for his Kotoamatsukami to reset, which implies that Kotoamatsukami is an ability that has existed before in the past. After all, Shisui hadn't been alive yet long enough to use it even once, meaning that he must have gotten the knowledge of Kotoamatsukami's recharge duration from someone else who had used it before, someone who was probably a relative or ancestor who passed that knowledge of Sharingan lore down to him, thus why he and Itachi were aware of the Kotoamatsukami's limited number of uses.