The complex plane of alternate universes (異世界の複素数平面 Isekai no fukusosū heimen) is a concept in Cardfight!! Vanguard i. It is a model proposed by Kairos of tracking the multiple alternate universes of Planet Cray, comparing them by the amount of influence the demiurge has had on them.
In this model, each parallel timeline of Cray is plotted on the complex plane. Universes assigned positive real numbers are fully under the demiurge's control; not only are they considered canon, the demiurge promotes the characters and stories from these worlds the most. Universes that deviate from the positive real number line are not fully under the demiurge's control; they may be influenced by the demiurge, but primary responsibility for these timelines lies with other creator entities. Universes whose numbers have a real part of 0 or less have no direct influence from the demiurge. Cray i is the primary example of such a universe, having been created by Hazur with Kairos's help.
As Messiah is the deity favored by the demiurge, universes with positive real parts have a stronger Messiah influence. Universes with negative real parts are presumed to be strongly influenced by Gyze, although not much is currently known about Gyze-dominated universes, as only one, Negative Cray, has been extensively documented by Gear Chronicle.
Gear Chronicle is the primary organization responsible for administering to and tracking these timelines, although since the technology for traveling to parallel timelines has been made public, anyone can choose to investigate these timelines on their own if they so wish.
List of universes by complex plane number[]
- 1: The prime Cray. The timeline in which the original Cardfight!! Vanguard anime, Cardfight!! Vanguard G, and Cardfight!! Vanguard overDress take place. After the demiurge was defeated in Cray i, he retreated from this Cray to create the reboot Cray, although he did not relinquish his control over this timeline and eventually returned to it during the Chakrabarthi Divine Era.
- 1.6: The timeline in which the Cardfight!! Vanguard manga takes place. Shares similarities to the prime Cray and the reboot Cray, but has more similarities with the latter, which causes it to be slightly closer to that timeline.
- 2: The reboot Cray, also known as "the world of V." The timeline in which Cardfight!! Vanguard (2018) takes place. Little is known about the Cray of this timeline, although agents from Cray i have been sent to investigate it.
- |2 − x| < ~0.2: Timeline distortions have created a small cluster of universes surrounding the reboot Cray. These universes are where Cardfight!! Vanguard Extra Story -IF- take place. Agents of Cray i have been dispatched to investigate these distortions.
- |1 − x| < ~0.2: At least one distorted timeline was located closer to the prime timeline, noted for being one of the few interactions the demiurge has had with the original Cray since the creation of the V timeline.
- i: Cray i, the alternate timeline of Cray created by Hazur with Kairos's help.
- ~0.2+0.8i: The timeline in which Another Vanguard: Star Road Asuka takes place.
- −1: Negative Cray, a version of Cray where Messiah was the one who turned evil during the Cataclysm instead of Gyze. Here, Gyze is the deity who watches over the planet instead of Messiah. Gyze is significantly more active than Messiah, and as a result, the political situation of Negative Cray is entirely different; Negative Cray has no clans, with the main political units being the nations. Negative Cray was also attacked by Planet Brandt like the canon Cray, but unlike the canon Cray, the inhabitants of Negative Cray counterattacked Brandt and inflicted massive damage on it, forcing it to escape to the i timeline.
- 0: The Plane of Concepts, a Void realm where the demiurge created the blueprints of Cray. Various discarded concepts from Cray's creation exist here.
- −i: Unknown.
- −∞: A timeline where Gyze escaped the demiurge's control and succeeded in destroying Cray and Earth, severely wounding the demiurge in the process. Having gone insane and finding fault in all creation, the Gyze of this timeline now travels the universe destroying other planets.
- ∞: A world where Messiah went insane and escaped the demiurge's control, continuing to constantly create and create without being able to destroy. As a result, Cray became a massive, densely packed Katamari-esque mass where it is impossible to die, with all of its denizens clustered together and in constant pain and agony. Number tentatively assigned by Gear Chronicle. [DATA EXPUNGED]