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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 Ryōan-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.

The abstract of the original Nature article is available here, and somebody has posted the full PDF here.

Sean Michael Ragan

I am descended from 5,000 generations of tool-using primates. Also, I went to college and stuff. I write for MAKE, serve as Technical Editor for MAKE magazine, and develop original DIY content for Make: Projects.


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Comments

  1. Namban says:

    First of all, I’m really confused as to why this is posted on MAKE.
    Like a lot lately, it seems to have no connection whatsoever to Makers.

    But I commend them for posting this anyway- the thing is, my degree is in Japanese language and literature. And I love MAKE Magazine! Much of the paper’s explanation makes no sense to a layman like me. It seems you have to be a pattern analyst to understand it.

    I will say this- I have lived in Japan, and been to Ryoanji’s garden in Kyoto. And with my degree came analysis of Japanese gardens and their structure. There is actually a well known Buddhist principle that directed the building of the garden, and it’s meaning. The paper ignores this part of the layout’s meaning- the part about one rock being behind the others.

    You see, the subtle thing about this famous garden is the SIZE of the stones as well as their placement.

    The garden’s stones were designed to be purposely obscured by the others.The garden itself is a buddhist lesson- it was meant by design to represent the “cloudedness of mankind’s perception of reality”- the idea was that mankind only thinks it perceives reality fully, but that reality is never fully known by man. The idea that, at any given time, we cannot perceive all things at once.

    This garden was designed so that you cannot see all 15 stones in it supposedly from all possible viewpoints on the ground, even around the garden if you were a monk that had to go out and rake the stones (normal viewpoint is only the veranda view in the photo, the rest off limits unless you are a raking monk out in the garden). That was the major reasoning in individual rock placement- to teach this lesson to the monks in the most concrete manner possible.

    The layout of the rock groupings themselves being somehow symmetrically layed out on a certain branching pattern seems to be what they are arguing in the paper, and may be complementary to what I described. I will have to read it again a few times, but the original meaning behind the design was to teach that lesson.

    Whew! Things are not as simple as they seem when it comes to Japanese gardening- even green gardens all have massive amounts of object placement symbolism, often features are connected with mythical places/concepts, or have historical mimicry of famous Noh play scenes. It’s difficult to describe it all, but that’s the real meaning intended by Ryoanji. Just ask one of the monks in Japanese there!

  2. mgmitch says:

    The pattern also could be created by waves reflecting from the rocks and the lines created by the interaction as the reflected waves met.
    I like this better than the burn example

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