The need to fully occupy all solutions provided by the outermost set of curves will give the Octet Rule.
When the outermost curves overlaps with a inner curve, then, because two solutions on the inner have to be included before the last pair of solutions on the outermost curves can be included, the remaining two solutions on the inner curve must also be filled, in order to satisfy the complete solution criteria. This makes twelve solutions for a stable configuration; the Duodectet rule
However, as we move further in, there is a 16 particle rule, then a 20 particle rules, but no 18 particle rule, as each loop pair of the curves provides 4 solutions.
Furthermore at the other end of the line, Rule of 2 is possible if we prohibit the lower solutions as being too close to the center. In reality, the particle at the center extends a finite distance \(x_a\).
And the Rule of 4 will be filling one loop pair of the set of curves. This is a stability criteria only if this loop pair is the outermost pair, in which case the whole solution curves are being filled.
Have a nice day.
