The rope (the visual stimulus) did exist, therefore it was not a case of seeing something that didn't exist, rather it was a case of mistaken identity. The illusion of a snake was not created out of pure nothingness. How can a magician do a card trick illusion without a deck of cards? An illusion does not appear in absence of a stimulus.
From Wikipedia:
"The term
illusion refers to a specific form of sensory distortion. Unlike a
hallucination, which is a distortion in the absence of a stimulus, an illusion describes a misinterpretation of a true sensation. For example, hearing voices regardless of the environment would be a hallucination, whereas hearing voices in the sound of running water (or other auditory source) would be an illusion."