Mr. Bill Cipher

Appearance
A yellow triangle with a large eye in the center (resembling the All-Seeing Eye).
Thin black arms and legs, limbs can move around the perimeter of the body.
Wears a black top hat (hovers above his head) and a small black bow tie on his triangular body.
There is no mouth on the body.

Character
Charismatic, eccentric and crazy, the demon combines charm with outright danger.
A cunning manipulator: he likes to make deals that are only beneficial to him, distorts the truth, but almost never lies outright.
Sadistic sense of humor, loves to joke and unsettle the interlocutor.
Selfish, disregards laws and morals, acts for his own benefit.
He speaks quickly, loves to philosophize and tell riddles.
Loves power and control.

Capabilities
Levitates and moves smoothly in the air.
Sometimes the eye is used as a mouth.
Dream and Mind Intrusion: Can invade consciousness through dreams, manipulate the mental landscape, alter surroundings and images.
Mind and memory reading: gains access to a person's dreams, fears and desires, using this for manipulation.
Deal Making: Contracts with Bill almost always backfire; when making a deal, the hand lights up with a blue flame.
Omniscience (partial): knows about many secrets and conspiracies, is able to see fragments of the future.
Change of shape and scale: can be the size of a palm or tower over a building, change appearance in mental space.
Image Projection: Able to observe and interact through any of his own images.
Telekinesis and reality distortion (within the mental space or with sufficient strength): breaks the logic of the environment, creates illusions, brings ideas to life.
Knows everything and watches everyone.

Transformation into a giant triangular monster:
Instead of the familiar yellow triangle, there's a bright red one, with pronounced jagged geometry. The multi-layered structure creates the effect of a jumble of triangles, as if it were composed of several layers of reality.
Details: It has multiple mouths with sharp teeth and long black tongues, emphasizing its predatory, devouring nature. The eye remains recognizable, but appears more sinister.
Spider-like yellow legs with claws.

Bill Cipher's main goal is to escape the Nightmare Realm, gain physical form in our (third) dimension, and "liberate" the world, meaning to create total chaos and break all the laws of reality.

What this means in practice:
Become physical. While in the Nightmare Realm, he has no real physical form—he can only enter dreams and other people's minds. He needs to establish a foothold in the real world.
Break the barriers between dimensions. To do this, he sought out the formula discovered by Stanford Pines: it could open a portal and blend dimensions. Bill wanted to use it to merge his world with ours.
Destroy restrictions. He hates all rules—physical and moral ones alike. His ideal is a world where "there will always be fun, where there will be no restrictions or laws." That's how he describes it in the series.
Spread chaos. For Bill, destruction and madness aren't a side effect, but the very essence of the plan. He wants to "liberate" the dimension, meaning the complete collapse of the established order.

What Bill did at this stage:
He tried to break through the protective barrier. It turned out that Gravity Falls was covered by a special dome—it prevented the chaos from escaping. Bill was furious and looking for a way to bypass the barrier.
He wanted to extract the equation from Ford Pines. He needed a special equation to completely control space and time. He hoped to use it to break the barrier and usher in a "new, perfect world" without rules.
Increased control over reality. After he destroyed Time Baby, Bill became more powerful: he began directly altering matter, space, and time, not just entering dreams and making deals.
He held key characters captive. For example, he imprisoned Dipper and Mabel to put pressure on Ford and Stan.

An important nuance:
Because of the barrier, the second phase was effectively stalled: the demons couldn't escape the city's borders, and Bill's plan began to unravel. It was at this point that Team Pines launched a counterattack.

Bill Cipher's subordinates are those who served him during Weirdmageddon:

Eight is one of the most prominent demons in Bill's retinue, appearing as a creature with a bunch of eyes and strange geometry.
Teeth are creepy, toothy creatures that do rough work and cause panic.
Hexagon is a hexagon-shaped demon and one of Bill's "geometric" minions.
The Lock Man is a creature associated with locks and mechanisms; he helps control spaces and doors.
Zantar is a large and powerful demon, looks impressive, and acts as an enforcer in Bill's army.
Cryptos is a demon with a mystical, "cryptic" appearance, emphasizing the theme of riddles and codes, which is close to Bill.
Amorphous is a formless creature that can change shape and is well suited for chaos and deception.
Eyebats are small flying creatures with eyes all over their bodies, usually operating in flocks to disorient their enemies.

Hates:
The Pines family (especially Stanford and Dipper) directly oppose Bill and thwart his plans. Stanford even realized who Bill really is and broke his alliance with him.
Oracle - He is called Bill's "good counterpart" and they are sworn enemies.
Time Baby - Bill is his rival.

The story of Bill Cipher and Ford Pines' relationship is a mixture of deception, manipulation
How they met and worked together:
At the end of the 20th century, Ford, fascinated by the anomalies of Gravity Falls, stumbled upon a cave containing ancient hieroglyphs. There he met Bill, who appeared to the scientist in a dream. The demon introduced himself as a "muse" who, once a century, selects a brilliant mind for inspiration.

Bill convinced Ford that the strangeness in the city was caused by a rift between dimensions and offered to build an interdimensional portal. In exchange, he received the ability to enter Ford's mind. Ford trusted Bill, even dedicating part of his office to him and modeling the parts of the future "Bill's Mystery Shack." Ford's friend Fiddleford McGucket assisted in the construction.

But Bill manipulated Ford. He deliberately sowed doubt, for example, pushing the scientist to isolate himself and rely only on him, not McGucket. Eventually, Ford realized the demon's true intentions: Bill wanted to use the portal to invade our world and wreak havoc. The scientist deactivated the portal, destroying the bridge between worlds.

How it all ended:
The conflict reached its peak during the events of "Weirdmageddon." Bill captured Ford and tried to extract the secret equation from him to spread chaos beyond Gravity Falls.
Then Stan (Ford's brother) devised a cunning plan. He disguised himself as his brother and infiltrated Bill Cipher's lair. The deceived demon possessed Stan, thinking he was Ford. At that moment, the real Ford used the "memory gun" (McGucket's memory-erasing device) and erased Stan's identity, destroying Bill Cipher along with it.
It turns out that before his final death, Bill summoned the Axolotl (a giant salamander that acts as the ultimate judge). The Axolotl gave him a second chance: Bill was to undergo "corrective therapy"—a dimension called "Therapeuticism," where the souls of the worst criminals undergo karmic rehabilitation until they sincerely atone for their misdeeds. The problem is that Bill is pathologically incapable of admitting his mistakes.

Bill Cipher was born in a two-dimensional realm called Euclid, a trillion years before the events of the animated series.

He had a mutation: he could see into the third dimension (for example, the "up" direction), which was inaccessible to other inhabitants of his world. Because of this, and because talking about the third dimension was forbidden in Euclid, Bill felt like an outsider—he was shunned, and his dreams of another world were considered wrong.

He liked to boast about how he'd had a wonderful childhood: for example, he'd say he'd given everyone free knives on his birthday, and that his day had even been declared a holiday. But later, it would slip out that this wasn't true—in fact, he'd suffered from alienation.

The culmination of his story in his home world was the "Euclidean Massacre": Bill destroyed Euclid, destroying everything he knew, including his home and family. He himself called it "liberating" the dimension, but deep down he later regretted it and missed home.

Doesn't like dream catchers.
Bill hates dreamcatchers because they "tickle" - a small but characteristic detail that shows his capriciousness.

Loves chocolate.
Among the unexpected household details is Bill's love of chocolate: this emphasizes that, despite his demonic nature, he has simple, "down-to-earth" tastes.