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The Waterman butterfly is built from eight lobes, one for each eighth of the globe, and every piece is projected separately. That is why distortion does not build up toward the poles, as on cylindrical maps, but toward the edges of the lobes. The Tissot indicatrices show it clearly. The smallest and roundest lie at 30° latitude, at 30° and 150° longitude, near the centers of the lobes. At 60°, at the same longitudes, area is about 30% larger. Almost twice the area belongs to the ellipses on lobe boundaries: on the equator, where the northern and southern lobes meet, and in the northern hemisphere at 90°E and 90°W. The four northern lobes meet at the North Pole, in the upper part of the map.
In every uncut ellipse angles change by about 10° at most, so land shapes are very faithful here. Six ellipses at 90°E and 90°W, from the equator southward, are crossed by the gaps between the lobes, though. Each of them is split into two parts in different places on the map, and a country outline dragged across a gap breaks up the same way. Antarctica is cut into four pieces that end up at the tips of four different lobes.
Drag Poland from its place to the equator, around Uganda, and it grows by about half, although on cylindrical maps it would shrink there. Australia lies near the center of a lobe and is one of the least enlarged landmasses here. From the center of a lobe to its edge, area grows by roughly a factor of two at most, which is a very good result for a world map. The price is having to read the map in pieces, across the gaps that cut through the oceans.
Eight, one for each eighth of the globe, with every piece projected separately. That is why distortion grows not toward the poles, as on cylindrical maps, but toward the edges of the lobes. The four northern lobes meet at the North Pole.
From the middle of a lobe to its edge area grows roughly twofold at most, a very good result for a world map. It is smallest at 30° latitude near 30° and 150° longitude, and about 30% larger at 60°.
The gaps between lobes cut it into four parts that land at the ends of four different lobes. Any outline dragged across a gap falls apart the same way: six Tissot ellipses at 90°E and 90°W are split too.
Yes, in the uncut ellipses angles change by about 10° at most. Poland dragged to the equator near Uganda grows by about half, although on cylindrical maps it would shrink there.
