There is no stated link between Patronuses and animagi
In canon there appears to be some kind of "one animal per person" rule. The only people where we know both their animagus form and their patronus are James Potter (stag) and Minerva McGonagall (cat), and in these two cases they match. Additionally, Remus Lupin, a werewolf, has a wolf for a patronus and Dumbledore, who is very close to Fawkes, has a phoenix.
Unrelated conclusion: fursonas are HP canon.
New chapter!
This is a new thread to discuss Eliezer Yudkowsky’s Harry Potter and the Methods of Rationality and anything related to it. This thread is intended for discussing chapter 104.
There is a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author’s Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: