Each ball would have a corresponding needle valve -
"There would be no way to direct and control the air pressure from a single tank." <-- um, you can - that was the point.
Picture is worth a lot of typing … so here
microcontroller, wires, needle valves, hoses, a single tank and a single compressor would be the list of parts.
The limitation would be on the microcontrollers ability to provide enough PWM signals - it could be multiplexed but you begin losing individual control (resolution) of the ball movement. But that would be an issue depending on what images you want to make
I realized that my previous picture of needle valves are not electric - here is a more appropriate picture
I have only seen the bernoulli effect in action with something like a reverse vacum cleaner that was supplying a large and constant flux of air. I assume that the design above would allow for a quick flux of air and then the ball would settle back quickly on the nozzle.
It really comes down to the level of detail the images need to have. 2 level imaging restricts you to basic silhouettes, lettering characters, etc.
The “Box Dance” video does in fact use graded values for height; you can see this by observing the pixels near the center - many of them never reach the full height of the other pixels. If you were to attempt a smoothly propogating wave with binary pixel values you’d need to carefully match the wave speed to the rise/fall time of each pixel. For an actual image to move across the screen without blurring the edges you’d need to ensure the movement period (seconds per pixel) was sufficiently below the rise/fall time of each pixel.
If you use micro servos, geared motors, or similar then there is virtually no overhead involved with adding shading. With other designs there will be significantly more added cost and complexity.
As far as the Bernoulli effect design goes you’d need to ensure that each ball was isolated from the surrounding ones, otherwise the venting of adjacent valves would disturb the ball’s stability. For the balls to become trapped in the air stream the valves must also open and close gradually, otherwise inertial effects will shoot to ball out of the stream, or at the very least generate excessive turbulence. The only way I can see this working effectively is if the balls are either contained in transparent tubes, or if they have a small area of open space around them and they are securely tethered to the valve, preferably with an elastic cord. The second of the above options will require a significant amount of extra air pressure compared to the first option, due to various turbulence and loss effects.
