You don’t need much to do a persistence of vision display. A few LEDs and a processor is all it really takes. [B45i] made a simple PC board with five LEDs and an ATtiny CPU. There’s a battery and it connects to a fan to spin around.
While the project is pretty simple, we liked two aspects of it. First, he provides very detailed explanations about how to use an Arduino to program the Tiny using the Arduino IDE.
The other item of interest is the two web applications that can build arrays of data for the POV display easily. Examining the code is instructive, too, because of the use of bit coding and enumerations to save space.
The downside, however, is you do have to adjust the delay to match the fan or other rotating item you attach to. It would be a great enhancement to read an accelerometer and adjust the speed on the fly. That would, however, drive the costs up a little bit. You would also need a clever way to drive the LEDs since you’d lose at least one pin to the accelerometer.
You can make much more sophisticated POV setups, of course. You can even do it with an FPGA.