Art Transformation and Representation of Game Go

Kun Zhang¹, Songlin Zhang ²

¹ Key Laboratory of Geographic Information Science, Ministry of Education, East China Normal University, Shanghai 200062, China (kzhang@geo.ecnu.edu.cn)

² Department of Surveying and Geoinformatics, Tongji University,

Shanghai 200092, China (zhangsonglin@mail.tongji.edu.cn)

Abstract: As one of Chinese four arts, Go is not only a competitive game, but also a syntheses reflecting many aspect of our life. With the development of computer techniques, people heavy use computers to study Go. It seems that most effort are used in programming more intelligent software to play Go. In this paper, we put emphasize on interpreting graphics comprised of black and white stones, scripting language is employed to transform 2D graphics into 3D forms.

Keywords: Go; Art; Transformation; Spline

Generative Art is the art of transformation. Transforming mathematics into images^[1]; Transform ASCII character into virtual reality scenes^[2]; Transforming bridge arches into Wupeng shape^[3]; Transforming cellular automata into Music^[4]; Transforming music into spatial forms^[5]; Transforming culture and historic elements into architecture^[6]. By the aid of computer techniques, most of the art forms could now be stored in digital forms and provide the possibilities to transform each other. The challenge is to find new kind of arts which will be taken as the source to generate other forms of art.

1. Game Go

Go (Weiqi in Chinese) is invented by Chinese between 3000 and 4000 years ago. In ancient China, Go was one of the Four Arts, along with music, painting, and poetry. Rule of this game is very simple, while the practical strategy is extremely complicated. Figure 1 shows the Go board and the playing of stones.

Figure 1. Go board and stones

Go board has a regular grid of 19 horizontal and 19 vertical lines. There are 361 intersections on the board and the stones are placed on the intersections as shown in Figure 1. Go is played by alternately placing black and white stones on the vacant intersections. A stone is captured and removed if it is tightly surrounded by stones of the opposing color. Figure 2 demonstrates four situations in which black stones will be captured. If it is white turn and white stone plays at A, black stone loses its last liberty and is captured and removed from the board.

Figure 2. Black stone being captured

A block of stones is survived if it has at least two inner liberties (holes). As shown in figure 3, two blocks of black stones are live with two holes. For no matter white player plays stone at A or B, there is another liberty for black stones.

Figure 3. Black stone lives

The objective of the game is to control a larger territory than the opponent. The players stake out areas that they want to own, while the opponent tries to push and squeeze those areas in order to gain more territory for himself^[7]. Both players try to capture opponent’s stone while placing their stones so they can not be captured. When a game is finished, each intersection is claimed by either black or white player. A player's score is the number of empty intersections enclosed only by his stones plus the number of intersections occupied by his stones. The player with the higher score wins.

Figure 4. Guan Yu playing Go while having his wounds attended to

(from http://en.wikipedia.org/wiki/Go_(board_game))

Figure 4 tells a famous story occurred during 208~280. General Guan Yu once wounded from a poison arrow, the wound required the bone to be scraped. Without the use of anaesthetic, Guan Yu plays Go to distract himself from the pain.

Figure 5. Palace painting (from http://hn.art2008.net/new/wdqy.htm)

Figure 5 painted king Wangjing Li (wearing the highest hat) plays Go with his brothers during year 937~975. King Li and his brother Yi Li like arts very much, they often call together famous painters to draw palace life. This painting is interesting for there is a screen behind players and on the screen drawn another screen.

Go has a tight relationship with Chinese ancient philosophy, military strategy and Buddhism. Go is always considered a metaphor of male and female, good and bad, day and night which is true nature in Chinese ancient philosophy. The ideas in Go and military strategy are often crossreferenced due to their similarity. For example, dialectic methods of analysis are frequently used in both areas. In Buddhism, Go is mainly used as a carrier to realize the spirit of Buddhism, win or lose are not important, the aim is to think quietly and forget the outer world. Yanmei Hu said in his book Thinking about Go Culture :“People will regret one day for only take Go as a competition game.”

2. Historic victory review and transformation from 2D to 3D

Although Go was invented in China and later introduced to Japan, Japanese had developed this game very well and their skill had exceeded Chinese players for most of 20^th century. 1985 is a very important year in Chinese Go history. In this year, the 1st China-Japan SuperGo Tournament was held. In the public opinion of "Chinese must lose", Zhujiu Jiang first won five consecutive games, next, Weiping Nie defeated Kobayashi Koichi, Kato Masao and Fujisawa Hideyuki successively and won the final victory for Chinese team. Nie was then regarded as a national hero and he proved him a top-notch Go player in the 2^nd China-Japan SuperGo Tournament by defeating five Japanese super Go players consecutively and won another victory for China. Figure 6 and figure 7 shows the three endgames Nie played in the 1^st tournament.

Figure 6. Nie vs Kobayashi Koichi and Kato Masao

Figure 7. Nie vs Fujisawa

Despite the understanding of this game, the graph of the endgame is a art of itself. Black and white stones enwinded each other, it is a result of competition for more territories; It is a record of strategies and tricks of two minds; It is also a philosophy about depending, without black or white stones, the counterpart loses its meaning of existence. However, these three games are demonstrated and appreciated separately. We proposed a way to connect these games and to exhibit it in three dimensions, which we feel represent the nature of Go in some new taste.

We use 3dsmax (Autodesk) software to redraw Go board and stones. Boards are modeled using plane geometry with length segments and width segments both set to 19, and three boards are placed paralleled as shown in figure 8. Stones are modeled using oilTank geometry. We create a spline to connect the first stones of each game, and then create another spline to connect the second stones of each game, the process continues until the 50^th stones of each game are connected. Splines connect black stones are rendered by black color; Splines connect white stones are rendered by white color. Modeling such a scene by hand is a tired work and will take a long time. We employed Maxscript language to modeling boards, stones and creating splines. Board geometry is required to convert to editable poly, thus the coordinates of each grid intersection could be visited using Board.verts[index].pos property, where index indicates the position on board from 1 to 361. Splines are created using following codes:

s = SplineShape pos:pointA

addNewSpline s

addKnot s 1 #corner #curve PointA

addKnot s 1 #corner #curve PointB

addKnot s 1 #corner #curve PointC

updateShape s

where PointA,PointB and PointC are the n^th stones of each game. Figure 9 displays the 50 splines. We read about complexity of conflict in space and time from interlaced black and white splines. These splines could be extended by adding more games, games played in China-Japan tournament, games played in contemporary era, games played in ancient time. It is easy to imagine that these splines will make up a endless streams which bear the belligerence nature of human being and emotions like joy, sad, ecstasy and dismay generated from the game.

Figure 8. Go boards modeled and placed in 3dsmax

Figure 9. Interlaced Splines

Some changes of setting will generate different results. Splines could be densifyed by adding more stones. Vertex type of splines could be changed from corner to smooth, which will produce curved shapes as shown in Figure 10. If we rotate one of the board, the splines will change. Suppose only four angles (90°, 180°, 270°, 360°) are allowed for one board, for 3 boards, there are 16 possible different spline forms. For n boards, there are 4^(n-1) possible forms by our calculation.

Figure 10. Smoothed splines with and without boards

3. Conclusion

There are no game that contains so much recreation, culture, history and profoundity like game of Go. As simply as 19×19 grids, Go continues to attract millions of people around the world. With the development of computer techniques, Go not only attracts general players but also AI professionals. However, computer Go software are far from satisfactory, a beginner player can beat computer easily. It is time for us to put more notice on the art of Go. In this paper, we created spline forms in three dimensional space, these splines connect different games and represent the complexity of Go. We have some other thoughts but not implemented yet. For example, how to express the subtle situation on board? Could the changing situation be transformed into visible forms?

Reference

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