If you look at the blue shape on the right, in all likelihood you will immediately perceive a cube, slowly rotating.
Now press the Reset button and then the Stop button, so that we can view this undisturbed. If you view this for a prolonged time, you may perceive sudden perceptual reversal between the two cube orientations as depicted below at the right. There the front-back of the cube is clearly indicated by depth shading. In the Necker cube at the top, however, both orientations are possible. By the way: Perceptual reversals of a rotating cube are accompanied by reversals of rotation direction.
What to do
Once you have seen the sudden reversals, you can experiment. Can you “hold” one orientation? Normally, this is not possible. After 10 s or so, it should flip again.
By changing gaze direction, one can select a preferred orientation.
Reversals are somewhat likely to be induced by eye blinks.
There is an additional treat in this demonstration: if you press the Impossible button, the rotation is reset to the primary position, and a green rod is pushed from the left into the cubic wireframe. Is the final position possible? This is a case of an impossible figure, and not related to the Necker cube phenomenon. What is interesting though: for me, the impossible figure seems much less stabel than the Necker cube and undergoes more frequent reversals.
Why does the Necker cube reverse? First we need to appreciate that the percept of a 3-dimensional wireframe cube is already an interpretation, which our brain performs on the 2-dimensional visual input of a flat line image on the screen. Given this image, many interpretations are possible (for instance, many wire zigzags could cast this same shadow), but our brain chooses a cube as the most likely interpretation. And both orientations are about quite as likely (the top one of the two disambiguated figures is a little more often seen).
So we understand why we see a cube, but why does it reverse? I figure the two possible perceptual states as attractors in percept space. Once the percept “sits” in one attractor, it feels at home, but through adaptation the attractor becomes shallower. By any perturbation, be it blinks, eye movements or “top-down commands” the percept can move to the other, not adapted attractor, to renew this game.
The Necker cube has interested observers from many disciplines, because it seems to allow decoupling of seeing and perceiving: Although the image remains identical, the percept changes. There is a huge amount of literature on this, which I can't even begin to cover here. Long & Toppino (2004) gave a comprehensive review.
L. A. Necker was a swiss mineralogist. He discovered the reversals by accident when looking at the drawing of a cube-like crystal.
Necker LA (1832) Observations on some remarkable phenomenon which occurs in viewing a ﬁgure of a crystal or geometrical solid. London and Edinburgh Phil Mag J Sci 3:329–337
Long GM & Toppino TC (2004) Enduring interest in perceptual ambiguity: Alternating views of reversible figures. Psychological Bulletin, 130(5), 748–768
Thanks to Jürgen Kornmeier for a rewarding & relaxing collaboration and help in phrasing the above description.