Consider the following figure:
It is a circle with a number of points around the circumference. They are equidistant in the figure, but they do not necessarily have to be. Each point on the circle is the center of a smaller circle. Each point on that circle has a circle centered on it, and so on. You can keep iterating and adding additional circles on the points to infinity.
What I am trying to come up with is a way to determine a maximum radius for the point-centered circles for each iteration ($r_1$, $r_2$, $r_3$ in the figure) so that that the circles do not overlap with any circles in the current or previous iterations. (The red circles in the figure demonstrate the condition I am trying to avoid.)
Also, just like biggest circle does not have to have equidistant points, the subsequent iteration's points do not have to be equidistant either, and every iteration and every set of circles can be different.
Each circle can also have a different number of points. (I have just made them the same in the figure.)