Monsters, Inc. opened 25 years ago, on 2 November 2001. Computer Graphics World counted 2,320,413 hairs on Sulley, and every one moves. His fur is secondary action, "an action that results directly from another action", and in John Lasseter's rule it is "always kept subordinate to the primary action". Stiffer fur might seem safer, but as Ed Catmull put it, "If movement is too simple, then it stands out." So every hair had to follow the body. Then the animators pushed his arm into his side, where the camera can't see: they animate "to the viewpoint of a particular camera". The fur got trapped and tangled. Pixar's scientists hoped the animators would stop, and in David Baraff's words, "The word we got back rather quickly was, 'No. The animators will continue to do what they have always done.'" So Baraff, Andrew Witkin and Michael Kass taught the simulator to forgive: a pinched point rides "midway" between the surfaces and the tangles resolve "as soon as the surrounding geometry permits". It was "used extensively for dynamics simulations of cloth and fur" in the film. Kass later wrote the other half: "If an emotional moment demands stillness, the jiggle must come to a stop." And Catmull: "We've become more complex in order not to be noticed."

The creature and its fur are our own recreation, not a film character.

Which movie trick should we take apart next?

Sources: David Baraff, Andrew Witkin and Michael Kass, "Untangling Cloth", SIGGRAPH 2003 (Pixar); Barbara Robertson, "Monster Mash", Computer Graphics World, October 2001; John Lasseter, "Principles of Traditional Animation Applied to 3D Computer Animation", SIGGRAPH 1987; Michael Kass and John Anderson, "Animating Oscillatory Motion With Overlap: Wiggly Splines", Pixar 2008.
Sounds: our own, made in code (earshot, CC0).