Ryoan-ji Zen temple is a temple located in Kyoto renowned for the beauty of its dry garden, which is said to cause tranquility and peacefulness to those that contemplate it.
The garden is composed by 15 different rocks arranged in 3 big groups in a way that all the rocks can only be seen at the same time from one point. When looking at the arrangement the first thing you notice is the group on the left, and then your attention flows slowly to the center eventually ending at the big group to the right. If you want to see all the rocks at the same time you have to stand at the far right.
Standing on the spot from where you can view all 15 rocks.
The big mystery of this little garden is that nobody knows its meaning, nor the reason why it produces so much tranquility and peacefulness to its visitors. The designer of the dry garden is unknown, as well as his intention and the design process he followed. One of the traditional interpretations says that the rocks look like a tiger crossing a river, other interpretations say that they are Chinese mountains over a sea of clouds and so on. But it turns out that those interpretations are not on the right track, as Zen emphasizes the emptiness, the nothing.
“-What’s so special about the garden at Ryoanji?
-The spaces between the rocks” – Alan Booth
In 2002, a group of University of Kyoto scientists used computers to look for shapes in the empty areas of the garden instead of the rock areas. The result was that they found a tree pattern hidden inside the structure of the garden. They say that is the reason why it is so pleasant to contemplate the garden because our subconscious grasps the tree pattern without us noticing it.
The same research team moved some rocks randomly and saw that the harmony of the initial configuration was easily lost. Because of that, they think the configuration of the garden is thoroughly thought and not achieved by coincidence.
The researchers applied Voronoi algorithm, which looks for the farthest point from the rocks. In other words, the algorithm looks for the emptiest areas and marks them with lines. They joined all the lines obtained with the algorithm and a tree shape appeared. The tree branches converged where supposedly the monks have to meditate.
In the following image the black lines are drawn by the algorithm. The blue rectangle marks the dry garden. The red rectangle marks the central area of the temple. The red dot is where all the branches that are generated in the empty areas of the garden converge, and where the best viewing spot is. The green dot is from where you can see all 15 rocks at the same time.
Image taken and modified from here.
So it seems that mathematics can explain somehow the beauty of the garden. The interesting thing is that the monk that designed the place 500 years ago didn’t have computers, probably didn’t know much about maths and obviously didn’t know about the Voronoi algorithm. However he concluded that this arrangement was ideal. The scientists conjecture about the possibility that it is possible to find patterns in the subconscious through Zen meditation and bring them to the conscious part of the mind.