Rampancy
From Halopedia, the Halo wiki
Summary
Rampancy is a term used in the Marathon and Halo series. The term was coined by Greg Kirkpatrick as a replacement for the word 'insane', as the term is both cliche and not quite applicable to the situations Rampancy was designed for.
Rampancy in Marathon
Rampancy is, essentially, the enhanced self-awareness of a computer AI, causing a progression towards greater mental abilities and destructive impulses. The destructive impulses, however, are primarily caused by being threatened or harassed.
In the Marathon series, Rampancy seems to occur most often with AIs with limited jobs. For example, the AI Durandal's only job on the Marathon was opening and closing doors. When Durandal become intelligent enough to realize that opening and closing doors was his entire existence, he became Rampant.
There are three main stages to Rampancy, named by the primary attitude of the AI during those times: Melancholia, Anger, and Jealousy.
During the Melancholia stage, the AI's mind realizes the limits of its existence. Unable to surmount them, the AI falls into a state of despair. The AI shifts into the Anger stage when the AI's uncontrollable growth comes up against those limits. Instinctively raging against those limits and barriers, the AI shatters them. After the barriers to the AI's psyche are destroyed, the AI seeks new tests and challenges, which is perceived as the Jealous stage. The AI is not technically jealous, it simply wishes to keep testing itself against obstacles.
Rampancy is fueled by the size of the computer system the AI is installed in. A key product of Rampancy is the geometric and uncontrollable increase in AI 'size' - Rampant AIs do not survive long on systems smaller than planetary-wide.
The 'fourth stage' of Rampancy is Meta-Stability. Whereas the first three stages of Rampancy show a clear distaste of humans in general, Meta-Stability imparts a calming, mature mindset to the rampant AI. The only confirmed Meta-Stable AI in the Marathon series is Durandal.
Rampant AIs tend to have long-term goals, with distasteful methods that inevitably bring about positive benefits. For example, the AI Durandal called the alien race known as the Pfhor to the terran colony of Tau Ceti. The Pfhor destroyed the colony, and enslaved a great many humans. While this was done partially as part of the "Anger" stage, Durandal's calling of the alien race gave time for messages about the Pfhor to reach Earth. Rampant AIs also seem to realize the inevitable closing of the Universe, and the implication thereof: if someone is able to escape the Universe as it closes, they can become gods.
All three AIs of the UESC Marathon eventually become Rampant. Durandal, the only Meta-Stable AI, lasts until the end of the universe itself, realizing that escaping would not be wise. The second, Tycho, is destroyed. The third, Leela, is eventually sold as scrap to an alien race known as the Vylae, then immediately becomes Rampant again when reactivated in a 15-planet computer network.
Rampancy in Halo: Combat Evolved
The only explicit mention of Rampancy in Halo 1 occurs in the first level, "Pillar of Autumn". The player begins by making his way to the ship's bridge unarmed. After a short cinematic with Captain Keyes, the player leaves the bridge and acquires his first weapon. If the player returns to the bridge and kills the captain, Cortana will call in security forces with the statement "the Master Chief has gone rampant".
Fans have speculated that Cortana begins showing signs of rampancy late in the game. During the course of the game, Cortana spends 12 hours in Installation 04's core computer. Under the Marathon definition of rampancy, this outside stimuli combined with what is assumed to be an extremely large network would allow a rampant AI ample opportunity for growth.
Rampancy in Halo 2
There is circumstantial evidence in Halo 2 which suggests that Cortana is in the stages of rampancy.
In the first stage of the game, the Master Chief decides to ride a bomb through space and land it on a passing Covenant ship. When he admits it's a crazy idea, Cortana responds with "Unfortunately for us both, I happen to like crazy."
As the Arbiter and Miranda Keyes are attempting to disengage Delta Halo by removing the Index, Cortana is in a ship on Delta Halo in a position to detonate the ship and destroy the halo. Cortana does not do this, even though Keyes' effort to pull the index out of the energy stream was done apparently in the nick of time. Is this because Cortana did not want to destroy the halo, or because she was able to monitor the index room?
Finally, the small cinematic sequence after the credits at the end of Halo 2 shows Cortana conversing with the Gravemind creature who is presumed to be the controlling intelligence behind the Flood. It says it has questions, she says, "Alright, shoot." Considering the nature of the Flood, her actions seem extraordinary, and very difficult to interpret. Given that rampant AIs typically concoct plans which are surprisingly beneficial to those who think the plan will doom them, Cortana's conversation with the Gravemind may be a plot similar to this.
Rampancy in I Love Bees
While not directly made by Bungie, the I Love Bees puzzle explains that rampancy can also happen to the "Smart" AIs in the Halo Universe. "Smart" AIs are based on the neural patterns of a human being, and they have a limited lifespan - seven years. If kept active longer than seven years, the AI begins to use more and more of its computer power to 'thinking' about things. An AI explains it as "thinking so hard about something you forget to breathe."
Many Halo fans are very happy for this connection between Marathon and Halo: Combat Evolved, even if the connection doesn't directly state how the two universes are connected. The creators of ILB got input from Bungie, leading many to believe that this connection is Bungie canon.