A long time ago, I went to a church picnic, and there was a booth for spin art. The guy had a large barrel with a platform on the bottom that spun when it was turned on. We sprayed paint at white target attached to the spinning platform. The patterns created were beautiful.
The Spinning Platform
I built my spinning platform using a large cardboard box and the motor from a remote controlled car. The advantage of using a car motor is that you can also put it in reverse.
Getting the paint consistency right takes some experimentation. It has to be fluid enough to flow, but not too fluid.