Attractor Field

The Steins;Gate universe consists of numerous world lines, which can themselves be arranged within attractor fields. The physical theory used is based primarily on many-worlds quantum mechanics.

An attractor field is a cluster of world lines that lead to a single converging point. While each individual world line is its own thread and thus has differences compared to its neighbors, all of the threads are moving in the same direction, and ultimately make up a single yarn bundle, or previously mentioned attractor fields.

Attractor fields refer to the strange attractors of chaos theory. Even under the chaotic evolution of multiple worlds, certain events are more likely than others, so take place on a larger number of world lines. The effect is that groups of world lines appear to converge on particular outcomes.

Suzuha: "The world is made of world lines and attractor fields."

'Suzuha takes a red yarn ball out of Mayuri’s costume sewing set placed on the table. She holds one end of the yarn and drops the ball on the floor.'

She stretches out about a meter of the yarn in front of her face to show it to us.

Suzuha: "The world’s structure is like twisted yarn."

Suzuha: "[Countless] possible worlds are superpositioned, branching out infinitely."

''Suzuha: "The entirety looks like one piece, but at the micro level, the world is organized like thin intertwined threads. And at the end, those fine threads converge into one. The paths are different, but the ends are the same." —'' Chapter 6, Steins;Gate"The attractor fields theory is a theory explaining the structure of the world in terms of world lines and world line convergence ranges (attractor fields). The premise is that the world is not one of countless parallel worlds. No more than a single world line exists, and on that world line all events from the past to the future are determined. In other words, as long as the world line determines that “Mayuri dies”, Mayuri will die. This is a world line convergence. However, the world line is constantly fluctuating, and one may be transferred to another world line for some reason. On that world line, a possibility that “Mayuri's death” has not been determined is born. However, the moment a world line is transferred to another, the original world line disappears and nothing but the new world line exists, so ordinary humans cannot perceive this world line fluctuation. World lines other than the current world line exist only as possibilities, and bundles of similar world lines among these possible world lines are called α (Alpha) world lines, or β (Beta) world lines. These are original settings, created by the ingenuity of the production team. — Chaos;Head & Steins;Gate: Science Adventure Series Maniacs, translation by Arkifixoff"In addition, verbal discussion might refer to all Alpha divergences as an "Alpha World Line" or "Alpha Line", although the term "attractor field" would eventually be developed by Okabe as to easily discuss details pertaining to the bundles that are attractor fields.

Each attractor field detailed in the Steins;Gate body of works and its related forms of media are summarized below.

Omega


The Omega Attractor Field is made up of all world lines ranging from -0.000000Ω to -0.999999Ω divergence. The starting number is negative, hence the lack of a starting number on the Divergence Meter. Official source material shows that the proper way to write Omega World Lines is "-0", even though such a number does not actually exist.

Little is known about the future of world lines of this attractor field. It is vastly different from the others in that Rintaro Okabe does not found the Future Gadget Lab, nor does he know any of his friends except Faris. On -0.275349Ω, the only known world line on the Omega Attractor Field from Okabe's perspective, he participates in RaiNet AccessBattlers tournaments with Faris NyanNyan and is her lover.

It can be assumed that SERN will not complete its time machine on world lines of this attractor field, because the lab is not together to create the PhoneWave (name subject to change) and subsequently the Time Leap Machine. Furthermore, the presence of the Divergence Meter is ominous; it could imply that time travel and the existence of world lines will emerge in this attractor field, or else the Divergence Meter would likely cease to exist.

Alpha
The Alpha Attractor Field is made up of all world lines ranging from 0.000000α to presumably 0.999999α divergence. This is the attractor field in which the majority of Steins;Gate takes place.

On most iterations of world lines of this attractor field, Dr. Nakabachi's conference at RadiKan is cancelled due to a mysterious object crashing into the roof, causing panic throughout the city. Kurisu Makise holds a speech on the implausibility of a time machine in Nakabachi's place, and she eventually joins the Future Gadget Lab as a result of Okabe catching her interest. Further experimentation and the design of the PhoneWave (name subject to change) leads to the Time Leap Machine, and the attempt by SERN to take control of the result and the people involved to further their own goals.

The closer the divergence number is to 0.000000α, the quicker the final convergent result of the Alpha Attractor Field is achieved as the influence of the attractor field and its converging points is stronger.

The final convergent result of the Alpha Attractor Field is the completion of the SERN Time Machine and the enslavement of humanity in a dystopia headed by the Committee of 300.

Chi
The Chi Attractor Field is made up of two known world lines. The first one, 1.048599χ is exclusive for events in Robotics;Notes: Revival Legacy. The second and most notable world line is 1.049326χ.

This attractor field is a next-door neighbor to the Steins Gate World Line, and it is only possible to land on 1.049326χ if Rintaro Okabe decides against undoing Luka Urushibara's D-Mail and three extra days are spent in the Alpha Attractor Field. Notably, Luka will decide to time-leap, and eventually succeed in reversing the D-Mail she sent herself.

The final convergent result, nor the future of the Chi Attractor Field is known. This world line could potentially have a peaceful future since Okabe is brought to the hospital for a wound on August 21st 2010, much like on the Steins Gate World Line. He refuses to explain how he got the wound in this attractor field, however. The presence of the Divergence Meter is ominous; it could imply that time travel and the existence of world lines will emerge in this attractor field, or else the Divergence Meter would likely cease to exist.

Steins Gate
The Steins Gate World Line carries the divergence value of 1.048596%. As it is under the influence of both the Alpha and Beta Attractor Fields, it does not reach the final convergent result found in either field. Since this world line does not converge upon the Committee of 300 and SERN's dystopia, nor World War III, there was no need for Suzuha to travel back to 2010 on this world line.

This is the world line that Okabe mentions and ultimately wants to land on throughout the story. The main draw of this world line is its unknown future—World War III over Kurisu Makise's knowledge and SERN's dystopia are averted on it, as well as specific character deaths which were unavoidable on either the Alpha or Beta World Lines encountered in the main story.

On this world line the following pieces of Steins;Gate media take place:


 * OVA: Egoistic Poriomania
 * Holy Day of the Calamitous Birth
 * The Movie - Load Region of Déjà Vu

Beta
The Beta Attractor Field is made up of most world lines ranging from 1.000000β to 1.999999β divergence, with few exceptions. The first is "Steins Gate", which is divergence number 1.048596%, while the other two 1.049326χ and 1.048599χ are world lines part of the Chi Attractor Field. This is the attractor field in which the beginning of Steins;Gate and the majority of Steins;Gate 0 take place.

On most iterations of world lines of the Beta Attractor Field, Dr. Nakabachi's conference at the Radio Kaikan building takes place as scheduled, with Rintaro Okabe attending. Shortly afterward, Kurisu Makise is found dead by Okabe, and he in a state of shock sends a text message about it to his friend Itaru Hashida, unknowingly beginning his journey throughout time.

Most iterations shortly after this timeframe are known for Nakabachi stealing Kurisu's thesis and defecting to Russia, sparking an arms race to secure all known information on the late Kurisu as to successfully build a time machine.

Although SERN attempts to conquer the world in this attractor field like they do in many others, convergence will not allow success due to the arms race, as well as SERN's ignorance to the Lab's activities here.

The closer the divergence number is to 1.999999β, the more quickly the final convergent result of the Beta Attractor Field is achieved as the influence of the attractor field and its converging points is stronger, save for the three noted exceptions which are not necessarily bound to converging under the Beta Attractor Field.

The final convergent result of the Beta Attractor Field is World War III, fought over Kurisu's Amadeus data and time travel thesis.

Gamma
The Gamma Attractor Field is made up of all world lines ranging from 2.000000γ to 2.999999γ divergence. This attractor field appears in Hyde of the Dark Dimension.

On world lines of this attractor field, Luka Urushibara's mother when pregnant receives strange messages to her pager with a future date, ultimately resulting in SERN's ambitions of control finding success much earlier in comparison to world lines of the Alpha Attractor Field. Their covert influence in this attractor field is depicted as much stronger as well.

A notable difference in this attractor field is the fact that Rintaro Okabe and Mayuri Shiina are separated as childhood friends, likely due to information gathered from analyzing the future text messages. Okabe lives a ruthless dual-life in all known iterations of the Gamma Attractor Field, with many known details from the Alpha and Beta Attractor Fields reversed as a result of the aforementioned events.

The final convergent result of the Gamma Attractor Field is the completion of the SERN Time Machine and the enslavement of humanity in a dystopia headed by the Committee of 300, much like the Alpha Attractor Field. A grim difference here is that Okabe becomes a high-ranking member of said committee, ruling Japan as the dictator "Hououin Kyouma".

Delta
The Delta Attractor Field is made up of all world lines ranging from 3.000000δ to 3.999999δ divergence. World lines of this attractor field are noted for their seeming peacefulness, with neither the threat of SERN nor World War III as a looming threat. This is the attractor field where Steins;Gate: My Darling's Embrace and some world lines in Linear Bounded Phenogram take place.

While the PhoneWave (name subject to change) does exist much like as known in the Alpha Attractor Field, it is not central to the Future Gadget Lab's work in this Attractor Field and instead takes a backseat while they focus on the creation of more harmless Future Gadgets, such as "Darling, You Idiot!" and a dream-reading device.

It should be noted that SERN's influence is incredibly weak the closer the divergence number is to 3.999999δ, with known pawns of SERN from the Alpha and Beta Attractor Fields becoming completely safe individuals in higher Delta divergences who live fulfilling lives as ordinary people. However, as the deviation on the Divergence Meter dips lower, the presence of SERN seems to grow stronger and known members are once again living a secret dual-life. Even so, their influence appears to be particularly weak in any iteration of this attractor field.

Epsilon


The Epsilon Attractor Field is made up of all world lines ranging from 4.000000ε to 4.999999ε divergence, and was created for Steins;Gate: Linear Bounded Phenogram.

Trivia

 * In the anime Robotics;Notes, the series starts by showing the numbers 1.048596, those of the Steins Gate World Line on the Divergence Meter.
 * In the Robotics;Notes visual novel openings the numbers 1.048596 are also shown.