Maybe this should be called a “disco ball display”.
If you scatter some sparkle sparsely on an uneven black plate and illuminate it with a point source, each fleck of sparkle reflects a beam off in some quasirandom direction. If you rotate the wheel around its axis, the beams from different flecks will scan in a rotating pattern; if the light source is on the axis of the sparkle wheel, the pattern is a cone, but I don’t think that’s the case in general.
But I don’t care that much, because what I care about is what this looks like from a single, somewhat arbitrary point of view, an eye. It looks like sparkling, which is to say, brief pulses of light coming from apparently random sources scattered around the disk. If you watch long enough without moving your eye, the sparkle pattern repeats. Most of the glitter flecks have scan patterns that miss the eye entirely, but those that do not only illuminate it once.
If you map out the pattern of sparkling for a full rotation, you can turn the light source on and off at chosen times to select which flecks appear. With this approach, you can generate a moving image with a single LED, a glitter disk mounted to spin repeatably, and some sort of apparatus for reliably positioning your eye.
Multiple flecks that are simultaneously visible are a problem. If you illuminate while they are visible, you add noise to the image; if you do not, you have even lower efficiency. So ideally the number of flecks would be small enough that the average number of flecks simultaneously visible is somewhere around 1.0.
In the limit of perfectly parallel light, perfectly flat and infinitesimal flecks, and a perfectly infinitesimal viewing pupil, this would not be a problem, because each fleck would be visible for an infinitesimal period of time, so almost all would be at unique times. You could pulse the light source with a Dirac delta function in order to fit nonzero light into this zero time, so you could still see it.
But of course light sources have divergence, glitter flecks have size, flecks are curved, and pupils have size. Picking some numbers, a laser pointer might have 1.2 milliradians of divergence and 2mm of light source diameter, and might be mounted 2 meters from the spinning plate; glitter flecks might be 200 microns in diameter and not have significant curvature; and your eye might be “mounted” 1 meter from the spinning plate and have a diameter of 4 mm. Given these numbers, it seems like the 4-milliradian pupil is almost certainly going to be the limiting factor (and so you might as well use 4-millimeter or 8-millimeter flecks), but perhaps you could fix it by using a small (less than 2 mm) peephole.
You should be able to get up to 4π milliradians of angular scanning out of the apparatus, depending on the relative angles of the light, your eye, the axis, and the flecks. Unfortunately that still only gives you about 3142 pixels at 4 milliradians, which is a shitty display. Illuminating only part of the plate doesn’t help; spinning the plate faster doesn’t help; the issue is that you need each pixel to get its own separate timeslot in the rotation, and the timeslots are .004/(4π) of a full rotation. Making your pupil smaller will help, and if you can make different rotations different, that will help too.
If you add more light sources, that will help a lot, because the different light sources can activate different flecks simultaneously with no interference. Alternatively you could move the eye, the axis of rotation of the plate, or the light sources, in a controlled fashion, so that different rotations are different in a repeating pattern. So, for example, if you use an 8x8 array of light sources, a 2mm peephole, and rock the axis of rotation of the plate around at 4× slower than the rotation of the plate, you might be able to get 3142·8·8·2·4 = 1.6 megapixels. Now we’re talking!
If you rotate the plate at 5400 rpm (90 Hz) and revolve its axis of rotation at one-fourth that, you get 22½ “frames” per second.
You might think that the contrast ratio between the glitter and the black background will be a problem, but I think that you can enhance that contrast ratio arbitrarily by getting further away — until the beam from the glitter fleck is as wide as your pupil, at which point you stop winning.
Then it’s just a matter of mapping out which light source illuminates which spots on the disk at which position in the rotational cycle.
As displays go, this is grievously inefficient. If your disc is 50mm across and only the light falling on a 200-micron-square portion of it is being used, and that only half the time, then 62499/62500 of the light is lost. But with a sufficiently bright light source, that should be okay.
Using this approach backwards, you can recognize the fleck pattern of a particular position with a camera in order to detect the rotational position of the disc: a rotary encoder, potentially with three degrees of freedom.