Algodoo

Since those rings have quadratic attraction, the speed in which objects get pulled are exponential increased, therefore at the centre the amount of attraction (in a sense) is near infinite.

ie. closer=more power

Hummmm

The one that's placed at the center does not disappear, it is removed. When you start up algodoo it will automatically place 4 black remove planes around the origin of the game world. These are pretty far out so you will most likely not come in contact with them. The circle at the center of the larger circle is traveling so fast it will cover the distance in one instance or tick of the game engine, which looks instantaneous. It is traveling so fast because of the equation to find gravitational force which is F=(G*m1*m2)/d^2.
If your distance is very close to 0, you will get very large forces. If you remove the four walls you will see that it traveled into the third quadrant with EXTREME speeds. Hope I could help.