Just ran across this fascinating little paper published in Nature back in 2002 by Gert J. Van Tonder, Michael J. Lyons, and Yoshimichi Ejima. In it, the authors apply a simple shape analysis to the layout of the 15 boulders in Japan’s most famous karesansui (or “Zen garden,” as they are often called in the West) at the RyÅan-ji temple in Kyoto. The technique they use is called “medial axis transformation,” which, by my understanding, basically means that they took the Voronoi diagram of the boulders in the garden as viewed from above. The paper’s authors explain their method with an elegant analogy:
[I]magine drawing the outline of a shape in a field of dry grass and then setting it alight: the medial axis is the set of points where the inwardly propagating fires meet.
Their findings, nicely illustrated by the figure above, were basically that the negative space between the boulders is very carefully structured to form a simple, three-level, two-branch fractal tree, with the “trunk” aligned on the temple’s main hall, indicated by the red square, which is the traditional preferred viewing area for the garden itself. Random rearrangement of the boulders fails to reproduce these features, strongly suggesting that they are the result of deliberate design.