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When an animated character gets frightened, excited or angry, she may flail her arms or legs around so fast that they are literally a blur. Sometimes it's a complete blur; other times, you will see the arms or legs, but in multiple vision.
This trope comes in a few simple variations:
A character doing a Wild Take flails her arms, sometimes jumping in the air and flailing her legs, too. Occasionally, this will cause her to hover like a helicopter — or a hummingbird.
Tomo does this in the first episode of Azumanga Daioh upon finding out she's late for class.
This happens in an episode of Tokyo Mew Mew where Ichigo does this with her legs...until she slips on a piece of broken crockery.
Done in an episode of Dragon Ball, where Goku pretends he has a technique that lets him have eight arms. The trick, of course, is that he's waving them up and down so fast the after-image makes it seem real. This is in response to Tenshihan's technique of actually growing a second pair of arms.
This happens to many girls frequently in Fairy Tail, particularly when humorously distressed or angry. Lucy does this most often, and Coco from the most recent arc is guilty of this as well, running around the room and doing this as she talks to people.
Taiga, yet again a GenkiGirl, does this sometimes in Fate/stay night, at least in the game. She doesn't move her arms that fast though since Fate/stay night doesn't really use cartoonish body movements like that but Taiga's antics does push it sometimes.
The Simpsons has two rather literal examples of this; in one Halloween Episode, Krusty's pacemaker shorts out and gets set to Hummingbird Mode ("Nectar! Nectar! Gotta drink my weight in nectar!"). In another, we see security cam footage of Apu thinking he's some kind of hummingbird after working for 96 hours straight; he tip-toes across the Qwik-E Mart, flapping his arms and humming (he also says that he tried to drink nectar out of Sanjay's head).
Sometimes seen in Totally Spies! particularly when Clover gets really angry.