Rhombi Tiling

The graph is about rhombi tiling an octagon shape, created by R. Kenyon and A. Okounkov. Finally, I figured out how to read the graph.
The graph is planar 2-D shape. But there are three possible orientations for a rhombi, straight up, left and right. These three orientations are painted by three different colors. As a result, if you pick the color properly, the graph looks like a 3-D one (block buildings). The genius thing here is that the third coordinate does not come in a natural sense (for example, directly proportional to color or some other parameter). Rather it seems a visual effect only without deep meaning. They further proved that for the random tiling, the 3D graph shows some patterns: The borders of the 3-D building approaches to some functions. The idea seems crazy at its first sight. However, it works very beautifully. The understanding of the deeper connection seems not easy though.