What to see
Above you see a swarm of red moving disks. On closer inspection they organise themselves into a rotating sphere. This sphere may rotate left- or rightwards, and may even switch spontaneously, but that's another illusion ;-).
What to do
The relative brightness of the red disks versus the green background changes automatically (indicated by the vertical slider). At the extremes (bright red or dark red) the large sphere is pretty obvious. However, when the brightness of the red disks is the same as that of the green background – a situation called equiluminance – a number of interesting effects can be observed, namely: (1) the 3-dimensional percept loses salience; the sphere becomes nearly flat. (2) Some balls seem to flicker, especially those with large steps from frame to frame. I assume that the φ-phenomenon breaks down at equiluminance (this may be an original observation, I’m not aware of any publication on this).
You can grab the slider yourself to determine the most effective position (for me, that is around 150).
The visual pathway from the eyes to higher visual brain centers consists (largely) of two parallel streams, the “magnocellular” and the “parvocellular” stream. For our purposes here it suffices to know that the magnocellular stream, while being motion sensitive, is (nearly) colour blind. Thus, in equiluminance, the magnocellular system cannot convey any motion signals because it effectively sees nearly nothing. Thus there is no clear information to construct the global gestalt of a rotating sphere. [The colourblind magno pathway also plays a role in explaining the “stepping feet” illusion.]
The distinctions between the “magnocellular” and the “parvocellular” streams are frequently oversimplified & overstated (like by myself above :), and their relation to luminance and colour processing is not 1:1 (Cavanagh 1991). Many effects occuring at equiluminance are just due to the lower spatial resolution of colour processing (≈≈10× for red-green, ≈20× for yellow-blue). The demonstration above shows this: Reduction of dot size (e.g. to 2) renders the “vanishing” at equiluminance much stronger.
Cavanagh P (1991) Vision at equiluminance. In: Kulikowski JJ, Murray IJ, Walsh V(eds) Vision and Visual Dysfunction Volume V: Limits of Vision. CRC Press 234–250 [PDF]