Is there an electronic part that acts like a potentiometer, but floats randomly across different levels of resistance?
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You need to specifiy the voltage range across the pot.
Also, "floats randomly across different levels of resistance" is meaningless in the language of electronics, which , evidently is not your area of expertise or you wouldn't be asking the question phrased that way. Please clarify what you mean without using the above wording.
If I had to take a SWAG, I would say you are asking for a digital pot driven by a random number generator program but the problem is that digital pots typically only operate at 5V and not higher voltages so if the voltage in question were greater than 5V it wouldn't work.