@Max: "... the 16-NeoPixel Ring and 24-NeoPixel Ring..."
Either one of those rings, with associated pushbuttons, would make a God-awful nasty game of Simon! One could start out with arcs of 4 or 6 (16 or 24) to simulate the four buttons on the original game, then remove one at random from each arc in turn so that, for example, the second level would be 4-4-4-3-1 (five "buttons"), the next 4-4-4-2-2 (five "buttons"), 4-4-3-1-2-2, 4-4-2-2-2-2, 4-3-1-2-2-2-2, 4-2-2-2-2-2-2, and so on. You'd also have to change the colors as you go along, with the original four "buttons" (arcs) set as Red, Green, Yellow, and Blue as in the original Simon, and different colors for the "buttons" (arcs or segments) as you start spliting up the original arcs. At the start, hitting any of the 4 (or 6) pushbuttons associated with an arc/button would count as a push (i. e., hit any Red pushbutton when four Red lights are lit).
Not only does the melody get longer, but the potential number of tones/buttons gets larger! With 16 or 24 different tones to remember as well as the sequence, this would be one tortuous game -- not one for those afraid of failure!
Higher levels could randomize the initial setup.
Hmmm ... perhaps a trip to the Patent Office is in order!
That's not mind boggling enough. You need to at least alternately turn the rows on and off, so you get that illusion of falling. Or maybe put a hinge on one side and a screw motor on the other, so you can change the angle between the two mirrors, so it looks a tunnel go around turns. Or just fix a pivot point at one corner and use two motors; one on the horizontal axis and one on the vertical axis and creating a spinning vortex into the abyss!
EDIT: I think maybe off center cams would work better.
You can't really tell from the images above -- but in the real world, the last test (with the three strips of wood = 1.5" seperation between mirrors) has an amazing impression of depth -- when you look down over the mirror sitting on our kitchen table, it appears as though the lights keep on going right down to the floor.