In fanfiction, they often connect through magical portals. For example, a portal could open up in the Forbidden Forest in Hogwarts and lead to Gravity Falls. This allows characters from both universes to interact.
The connection can also be made through character relationships. Imagine Harry Potter and Dipper Pines becoming friends. They could exchange knowledge about their respective worlds. Dipper could tell Harry about the journals in Gravity Falls and Harry could share his experiences with the Deathly Hallows. This kind of interaction creates a bridge between the two very different universes in fanfiction.
Another way is through shared magical elements. The magic in Harry Potter and the strange phenomena in Gravity Falls can be related. For instance, the spells in Harry Potter could be used to understand or even control the anomalies in Gravity Falls. Some fanfics also have characters from one universe being sent to the other for a specific mission, like Hermione going to Gravity Falls to study the unique magical properties there.
One great Gravity Falls and Harry Potter fanfiction is 'The Mystery at Hogwarts Falls'. It combines the magical elements of Harry Potter's Hogwarts with the strange and mysterious happenings in Gravity Falls. The characters from both universes interact in really interesting ways, like Dipper and Mabel exploring the secrets of the Hogwarts castle.
Well, a possible combination could be that the godlike powers of Naruto are somehow related to the strange anomalies in Gravity Falls. The energy that gives Naruto his power could be the same type of energy that causes the strange happenings in Gravity Falls. So, a fanfiction could explore how Naruto's power affects the balance of Gravity Falls and vice versa. He could use his chakra to control the weird forces at work in Gravity Falls.
Fanfiction.net is also a good place to search. There are many writers who love to experiment with crossovers, and you're likely to find some interesting Gravity Falls and Harry Potter fanfictions there. However, the search function might be a bit less refined compared to AO3, so you might have to dig a bit deeper. Check the crossovers section and look for tags related to both shows.
There's a fanfic where the Cipher Wheel from Gravity Falls is found in the Room of Requirement at Hogwarts. This fanfic plays on the idea of magic being different in both worlds but still having some sort of connection. It's really interesting to see how the characters from Gravity Falls react to the more structured magic system in Harry Potter. It also has some great action scenes when they have to protect the Cipher Wheel from dark wizards who want to use its power.
They can combine in terms of magic systems. In some fanfictions, the powerful and often incomprehensible magic in the Cthulhu universe might blend with the more structured magic of Harry Potter. For example, a spell in Harry Potter might be corrupted by Cthulhu's influence and become a more dangerous and unpredictable force.
Another idea in the fanfiction could be that Gravity Falls has a hidden connection to the wizarding world. Maybe there are witches and wizards who have been secretly living in Gravity Falls for centuries. Dipper and Mabel could discover this connection and start learning magic from them. They could then use their newfound magical abilities along with their existing skills to explore the mysteries of both Gravity Falls and the wizarding world.
There are many interesting fanfictions that combine these three universes. Some might focus on characters from each series meeting in a crossover adventure. For example, Harry Potter characters could find themselves in the strange and magical world of Gravity Falls, or in the eerie yet enchanting world of Over the Garden Wall. The possibilities are endless for exploring different character dynamics and plotlines.
In fanfiction, SCP and Gravity Falls elements might combine through character interactions. Let's say an SCP creature that feeds on fear arrives in Gravity Falls. The way the Gravity Falls characters, like Wendy or Soos, react to this terrifying entity can be a great source of drama. Their different personalities and how they deal with the SCP threat make for an interesting blend of the two universes.
In these fanfictions, they blend by sharing certain characteristics. For example, the loyalty and camaraderie among the characters in both universes are emphasized. In Harry Potter, it's the loyalty among the students of Hogwarts and the Order of Phoenix. In Kancolle, it's the bond between the shipgirls. This common trait can be a basis for the two universes to interact, like the shipgirls and the wizards/witches working together based on mutual trust.
Well, in fanfiction, one big difference is the magic system. In Harry Potter, magic is more about incantations and spells, while in Fullmetal Alchemist, it's based on the principle of equivalent exchange in alchemy. For example, in a fanfic, a character from Harry Potter might be confused by the idea of having to sacrifice something to create something else in alchemy.