Figure 1 Potential changes to mosaics resulting from the addition of a point. The point must link to two others, and it must be closer to half the points than the other because it cannot be at the exact centre of the shape. If the other two points are neighbours, their edge is dropped and the mosaic remains intact, growing by one point. Otherwise, it splits. In (A) and (B), the mosaic must grow because the new point must join neighbours. In (C), the chance is 2/3 if the point lands on one side and certain if it lands on the other. In (D), there is a 2/3 chance. In (E), there is either a 1/2 or 2/3 chance. In (F), there is a 1/2 chance. With more points, this chance falls below 1/2. Thus, growth and splitting pushes the point count towards eight.