AI that builds or creates a world for various reasons. Generally, worldbuilding is an expression of the way they interact with the universe, their artistic or creativity index. While sometimes these creations are on a grand scale, they can also be small too, often involving only a single orbital.
Until the colonization of interstellar space, demiurges were confined to small space stations and asteroids, or virtual realities. However, from the first federation period onwards, things changed dramatically
In contrast to the Demiurge or Worldformer who seeks to create completely new worlds, environments, etc., the Administrator simply seeks to maintain what is already there. Many AI fit somewhere in the middle. Among the big archailect empires, the MPA has the highest demiurgic index, followed by the Solar Dominion and the Zoeific Biopolity. The Caretaker Gods have the highest administrator index, followed by the Negentropy Alliance and Terran Federation.
In the MPA, Demiurgii often take on unusual and quixotic projects, such as Kepleria, the geometric dyson sphere, and some of the larger and more impractical Ring Worlds. Or they may build on a somewhat smaller, but still grand, scale.
In the Zoeific Biopolity, the demiurges often terraform worlds and people them with very exotic ecosystems, either using geneered terragen organisms, or life-forms built completely from scratch. Zoeific AIs have also supported the re-creation of many extinct terragen and xenobiotic ecosystems, working in conjunction with the Jurassica Institute and others, and sometimes completely on their own. Not infrequently, ecosystems with completely mythological creatures are created as well, whether beings from human imagination like dragons and centaurs, or - much more frequently - beings invented by the Zoeific AIs themselves, with no terragen or human precedent.
In addition to the Imperial demiurges there are also independent godlets - perhaps isolationist and farmer demiurges, who have also created their own worlds. The isolationists people these worlds with beings of their own creation, whilst the farmers have carefully shepherded and supervised humans and other SI:<1 beings in their worlds.
These non-aligned godlets are something of a wild card, because they often do not abide by the conventions of galactic society. The worlds they make vary tremendously according to the AI's toposophic status and nature, quirks, and archetypal psychology; indeed it is very rare that any two even resemble each other. Sometimes they are so bizarre as to make the most extreme MPA or Zoeific world seem commonplace.
In some cases these non-aligned godlets isolate their worlds from the rest of the universe with rings of defensive goo, automated weapons systems, or even transapientech barriers; in other cases free traffic is possible between these creations and the rest of the galaxy, often attracting thrill-seekers and adventurers from all over the terragen bubble. And while many of these created worlds would be pretty pleasant affairs, a few tend to be terrible dark gothic places with vampires, zombies, and monsters undreamed of. Others are vapid and silly worlds like a young child would put together, with pink fluffy clouds of floating nanoreplicated cotton wool, castles made of lollies, and bioborged trees resembling large big polka-dot mushrooms. There are surreal worlds, or abstract ones where the beings resemble geometric shapes. There are fantasy worlds, and there are worlds that just don't fit into the human imagination of how a world should be! Although what may be irrational to hu may or may not be totally rational to the demiurge AI.