Tree Diagram

The Tree Diagram was a super-computer which, according to the best renowned scientists in Academy City, was the best in the world.

Use and Capabilities
This computer was loaded into the satellite, Orihime 1, to monitor many aspects of the city such as weather patterns and security. Once a month, it predicts the movement of the particles in the atmosphere of the entire globe and calculates one month's worth of weather in one go. The Tree Diagram Information Receival Center located in the 23rd School District, is the one communicating with Tree Diagram. They send requests to it and also receive information and data from the satellite.

Another use of this computer is to aid researchers with their experiments. This consent, on the other hand, is very difficult to acquire since the Academy City's Board of Directors are the only ones who are able to permit access to Tree Diagram. One permitted use of Tree Diagram was for the 'Level 6 Shift' Project.

Index Arc
During Touma's fight with Index (while being possessed by Johann's Pen), Index accidentally directs a Dragon Breath's attack to space and destroys the Orihime 1 satellite, destroying Tree Diagram permanently. Meanwhile, Academy City covers up this incident by announcing that Tree Diagram can't be contacted for an indefinite period.

Remnant of Tree Diagram
It was revealed in volume 8 that the core of Tree Diagram still remains, and that the satelite might be repearable if it is retreived. Several countries in the world started launching their shuttles to recover pieces of the satellite, and uses the ruse of "showing-off" their space programs to the world, and to prove their reliability to sponsors. However, Academy City was able to recover the most important part of Tree Diagram, The Remnant.

Awaki is sent to retreive it while Mikoto - after hearing that the satelite might be repared, tried to stop her on her own. During this incident Kuroko also met Awaki and fought her twice doing her job as a Judgment. Awaki successfully escapes, but is cornered and beaten by Accelerator who unexpectedly snuck out of the hospital at Last Order's request. The core is subsquently destroyed by Accelerator, and Tree Diagram is now beyond repair.

Level Upper Incidents
It is revealed that Kiyama Harumi requested to use Tree Diagram for certain calculations 12 times - for her search on curing her Child Error students, before giving up and opted to create the Level Upper Network instead for her calculations. It is later revealed to have been inspired by Mikoto's clones' Misaka Network.

Sisters Arc
At the end of her rope in trying to stop her clones from being killed in the Level 6 Shift. Mikoto decides that she will manipulate the calculations of Tree Diagram. Her plan is to manipulate it as so it will produce an error in a simulation between Accelerator and Mikoto fighting, and determining that the scientists will rely on Tree Diagram to recalculate the data, she will create a prediction that doesn't involve the Sisters.

She goes to the 23rd School District, and breaks into the Tree Diagram Information Receival Center. She discovers there that her plans have been ruined, as Tree Diagram has already been destroyed and yet the experiments continue. Mikoto later determines, that since the Tree Diagram calculated that Mikoto will be killed on a certain number of moves against Accelerator, she needs to die on the first move alone to ruin the experiment; knowing that the Tree Diagram is no longer available for recalculations, if such a scenario would occur.

Toaru Kagaku no Railgun Omake Chapter
In a short omake chapter, a bunch of scientists attempting to create the perfect imitation of Mikoto's physical appearance, discover that they have yet to learn what underwear Mikoto wears. They first try to use the Tree Diagram for calculating Mikoto's panites, but is denied by Tree Diagram itself, stating that they shouldn't use it for "stupid things".