Friday, May 27, 2016

Visualizing chess

Ootro Estudio is a firm based in Alicante, Spain, that offers graphic and furniture design and 3D services. Their latest project is an alluring piece of data art titled Arbor Ludi, which portraits the game tree of eight top chess players from the last century. Here's a description:
The selected players are José Raúl Capablanca, Mikhail Tal, Tigran Petrosian, Bobby Fischer, Anatoly Karpov, Garry Kasparov, Viswanathan Anand and current champion, Magnus Carslen. We chose players with different styles, so their game trees would display the contrast between them. 
To generate the game tree of each champion we used a database of more than 10,000 games. The number of games changes significantly for each player: Capablanca was the less active (596 games) and Karpov was the most active (3,374 games.) This difference in the number of games affects the final result of the representations. 
In order to transform the data into a tree shaped object we used an algorithm programmed with parametric design tools. This algorithm deciphers the topological diagram of all games of each player while it builds a three-dimensional tree whose growth reproduce the said diagram. 
Following this topological diagram, the tree starts with a trunk that represents the total amount of games of each player. From it, the principal branches of the tree emerge, and each one correspond to the first move of all the games, being the thick of each branch proportional to the number of times this moves have been done. In each node, it appears written the move corresponding to the previous branch. The criterion recurs with the next moves, so that new branches emerge which are the result of the different paths that the players have taken in all their games. Each step adds a level of complexity to the topological diagram.
A limitation of the project is that branches that represent identical moves are not positioned identically on the different trees. Therefore, comparisons between players are hard, if not impossible, even if you zoom in to read the labels. Regardless, this is a quite impressive effort, and it'd certainly look beautiful if framed and hanged on your office walls!


  1. The curious thing about this graph is that the top-right image resembles the map of Brazil, while the bottom left one is similar to the state of Minas Gerais.

  2. They are really beautiful but the meaning of the colors are not clear, I guess they mean white/black pieces (green being black, due to the nature of the two trunks) but there could be other ways of coding info on the tree trunks (more on this later).

    It would be great if there were a way to compare game trees. For example Fischer was a fervent 1. e4 player with white and very seldom played anything else while Anand favors 1. d4 with occasional 1. c4 or 1. e4 or even 1. Nf3. Carlsen plays different openings and sometimes deviates very early from current opening theory. His games against high level oposition are in average longer than Fischer's and Tal's.
    It would also be great if the game result were encoded in some way (or even better, position evaluation encoded as well). Also I'd love to peruse the trees from different angles.
    Having said that, it is an amazing project with lovely visual results!