Initialization: Draw a circle of arbitrary radius and center position. Arbitrarily select a point on the first circle and use it as the center of a second circle with equal radius. The first two circles are defined as legal circles.
The rules for generating additional legal circles are as follows:
Rule 1. Wherever two legal circles of equal radius touch or intersect, draw another legal circle of equal radius with the intersection point as its center.
Rule 2. Within every legal circle with center point p and radius r, draw another legal circle whose center point is also p but whose radius is r/2.
Figure 1 below shows the result of a recursive application of the above rules.