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A "flipping" optical illusion is an illusion that can appear in two different ways, so the image "flips" in your mind. Examples are the Necker Cube or the following ASCII illustration attemts:

     _______
 ___/___   /
 \ /    \ /
  X------X
 /_\____/ \
    \______\
Are the longer fins pointing inwards or outwards from the screen?

  ___
 /  /|
/__/ |____
   | /   /
   |/___/
Are these stairs on the floor or in the ceiling?

If you stare at such a 2D image, your mind makes up a 3D representation of it. The problem is that the figure is ambigous; in 3 dimensions, it can be interpreted in two different ways. These two interpretations are the ones your mind flips between.

A similar phenomenon (but not related to 2D/3D) is the Pretty Woman/Old Hag imgage

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