"I saw the whole man slowly emerge from the window and begin to crawl down the castle wall"
Winged Vampire
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In the literature, vampires often possess special powers. Common attributes are increased strength, perception and speed, and the ability to create a kind of trance in their victim. Other vampire powers can range from shape-shifting to mind-reading. Each of the Twilight vampires has a different special power, and they're all remarkably good baseball players.

Often, vampires gain additional powers as they age. One special power that many fictional vampires possess is the ability to fly. Although this idea has become somewhat iconic, Dracula in human form cannot fly (as indicated by his wall-crawling). He can, however, shape-shift into other forms, inspiring the often repeated motif of the vampire villain turning into a bat. 

Vampire abilities in fiction

The description of Dracula crawling down the wall is particularly horrifying, and has influenced similar powers in other fictional vampires, most notably the gifted vampires of Anne Rice’s Vampire Chronicles who can crawl up the sides of buildings. It is not clear, however, if Dracula’s wall-crawling represents such a power, or whether he is simply able to scale the wall at a preternatural speed; Jonathan himself does successfully scale the same wall, albeit much more slowly.