Figure 2 Mosaics of randomly located points within shapes having diameters of 1. There are 100 in each panel. (A) and (B) show the raw mosaic graphs; (C) and (D) include rectangles that indicate the contribution of each edge to the area estimate. (A) and (C): The shape is a square. There are 56 points with two edges, 38 with three, and six with four. There are 26 mosaic pieces, so the piece/point ratio is 26/100, close to the 0.25 prediction for a compact shape. The true area is 1 and the estimate is 1.098. The median over 1000 trials is 0.975. (B) and (D): The shape is a ring. There are 74 points with two edges and 26 with three. The piece/point ratio is 14/100, which is low because the pattern is elongate. The true area is pi/8 = 0.393 and the estimate is 0.373. The median over 1000 trials is 0.370.