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Despite its current use to describe any ominous dream, the term nightmare actually refers to the states known as the waking dream or sleep paralysis, usually associated with rapid eye movement. Through early European history these states were thought to be caused by demons such as the succubi or the hags. Collectively these female night demons were known as mara or mare and from this was born the word "nightmare".
In more modern culture, when personifying nightmares, artists and story tellers tend to take from the more modern term for mare, which is the given name for a female horse. Thus they are often portrayed as ghostly black horses often with manes of flame or smoke to represent their malevolent nature.