Most of the IC's you are looking for are actually a micro processor doing all the controlling via a internal program, You will find a range of premade circuits on Ebay and other places but doubt an off the shelf item will fit in the hoop, and you would need a purpose made board to suit.
Then you also need to fit in a power source (battery) of some form.
The important part would be to keep a weight balance within the hoop, and not a heavy blob all in one place.
Pete.