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. It served as a powerful computation device for many sectors of Academy City, before its sudden destruction due to unforeseen events.

Use and Capabilities
Under the pretext of weather prediction, Tree Diagram was loaded into the satellite, Orihime 1 (おりひめ1号), to monitor many aspects of the city such as weather patterns and security. The true reason it was loaded onto a satellite orbiting space was to protect it from external enemies, such as terrorists, human supremacists, and industrial spies.

The computer was so powerful that rather than forecast weather, it predicted it. 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, such as drug reactions, physiological reactions, electrical reactions, etc. Permission is very difficult to acquire since the Academy City's Board of Directors are the only ones with access to Tree Diagram. One permitted use of Tree Diagram was for the 'Level 6 Shift' Project.

The machine is so powerful that it would take 25 years for any other machine to catch up to its level.

Remnant
Remnant refers to the debris left behind by Tree Diagram after it was destroyed by Index on July 28th of the current year of the timeline. Specifically, it is the core of the supercomputer of the Tree Diagram that can be used to repair it.

Index Arc
During Touma's fight with Index (while being possessed by John'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.

Tree Diagram Remnant Arc
It was revealed that the core of Tree Diagram still remains, and that the satellite might be reparable if it is retrieved. Several countries in the world started launching their shuttles to recover pieces of the satellite, using the ruse of "showing-off" their space programs to the world and proving their reliability to sponsors. However, Academy City was able to recover the most important part of Tree Diagram, the Remnant.

The Level 4 Teleporter, Awaki Musujime, is sent to retrieve it while Misaka Mikoto -- after hearing that the satellite might be repaired -- tried to stop Awaki on her own. During this incident Kuroko Shirai also met Awaki and fought her twice doing her job as a member of 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 subsequently destroyed during the fight with Accelerator, and Tree Diagram is now considered beyond repair.

Level Upper Arc
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 opting 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 to produce an error in a simulation between Accelerator and Mikoto fighting, determining that the scientists will rely on Tree Diagram to recalculate the data and 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 the 185th move 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 occurs.

Toaru Anbu no Conference
In a short omake comic, 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 panties, but is denied by Tree Diagram itself, stating that they shouldn't use it for "stupid things".

In a humorous reference, Chapter 33 of the Toaru Kagaku no Railgun manga, during Mikoto's infiltration of the Tree Diagram Information Receival Center, a report is shown, among other things, referring to the request for Tree Diagram to calculate Mikoto's panties. Mikoto however, doesn't notice this.

Trivia

 * The Orihime 1 and Hikoboshi II satellites may be a reference to the launched by Japan on 1997, where two of the satellite's body is named Hikoboshi and Orihime.
 * Orihime is the Japanese name for Vega, part of the Summer Triangle together with and . The naming choice for it and the Hikoboshi II (Japanese name for Altair) may be a reference to.