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This article contains information on a subject that is not considered canon in the Gravity Falls universe.
He takes the form of a giant talking Axolotl.
Alex Hirsch AMA
As Bill Cipher is being erased from reality, his final words are a distorted, reversed message which says: "A-X-O-L-O-T-L! My time has come to burn! I invoke the ancient power that I may return!"
On the portal aperture page, Bill writes a cryptogram which translates to: "ILL GET THIS PUPPY UP AND RUNNING ONE DAY AND NEITHER TIME BABY NOR THE BIG FRILLY KNOW IT ALL WILL STOP ME" (Axolotls have their gills on the outside of their heads, giving them a frilled appearance).
Throughout Bill's Ciphers section, there is code which says: "CURSE THE AXOLOTL EVERY CONSPIRACY IS TRUE".
According to Alex Hirsch, the book is non-canon to the actual series, as it follows a "choose your own adventure" format, having many different possible endings. However, he also said it does contain "one enormous 'canon' secret".It is speculated that the canon secret could be Dipper and Mabel's encounter with the Axolotl in "the time and space between time and space". The Axolotl, a giant talking axolotl, lets each of them ask him a question. Dipper asks him "what [does he] know about Bill Cipher", to which he replies with a poem:
This suggests that when, before being erased from reality in the series finale, Bill gives a message that when reversed says "A-X-O-L-O-T-L! My time has come to burn! I invoke the ancient power that I may return!", he is actually invoking the Axolotl for redemption for his crime, and that there is one way to get absolved: he has to take "a different form" in "a different time". This would mean that Bill could return.
Sixty degrees that come in threes.
Watches from within birch trees.
Saw his own dimension burn.
Misses home and can't return.
Says he's happy. He's a liar.
Blame the arson for the fire.
If he wants to shirk the blame,
He'll have to invoke my name.
One way to absolve his crime.
A different form, a different time.
The line about "sixty degrees that come in threes" apparently refers to the fact that Bill's shape is an equilateral triangle: three sets of sixty degree angles (adding up to 180 degrees).
The Axolotl and Xolotl
A close relationship exists between the Axolotl and the aztec God of Weirdness, Fire, Lightning, Sun (formerly), Death, Twins, Deformities and Sickness Xolotl-Nanautzin. It is speculated that these two are probably identical. In Myths it is said that Xolotl once turned into an axolotl for not being killed by his own twin brother. Unluckly he was trapped in the sea he jumped and ended up forever being in this cage. But also Bill Cipher could be this god as well. Xolotl and Bill have many things in common, both want the apocalypse of weirdness, both have fire and lightning powers, both have something to do with twins, monsters, freaks and both are defeated emperors. Also both made many deals with other people.
It can also be noted that in the "Gravity Falls : Journal 3", on The Oracle's page, we can see in the background an Axolotl. Just above said axolotl is a code that, when decoded, says "The opposite of Bill". This line strengthens the theory of an opposite/twins relationship between Bill (Xolotl) and The Axolotl.