Yakumo Yukari's 800+-year-old kyuubi kitsune shikigami who specializes in black magic. She is also powerful enough to have her own shikigami, a nekomata named Chen, to whom she is portrayed to act motherly towards prominently in fanworks.
In volume two of Strange Creators of Outer World, it has been revealed that Ran is actually a shikigami parasitically taking host of a nine-tailed fox youkai so strongly that it never shows on the surface; leading people to not have any difficulty seeing her as a kitsune. However, this seemed to be subtlety hinted at in Yukari's Bohemian Archive in Japanese Red article where Yukari constantly repeats to Aya that Ran is a shikigami and not an animal.
Ran has been described to have a gentle personality and to be a lover of fried tofu like her kitsune body. She excels at mathematics and is able to solve nigh impossible equations instantly; simply seeing it as a hobby to kill time. She is rather robotic in nature when it comes to following Yukari's orders whereas Ran herself describes them as "Yukari's programming". Due to her master's prominent sleeping habits, Ran is usually doing her bidding at a constant. However, Yukari herself has stated that she would like to see Ran do something other than simply follow her orders.
Ran is simply seen as a tool that's loved in Yukari's eyes. If she is to ever stray away from her duties as a shikigami or to forget that she is one; she is to be violently disciplined, such as being beaten on the head by her parasol.
She is notorious in many doujins as a streaker, earning her the nickname "Suppa Tenko" ("Naked Heavenly Fox"), and for bursting into an epic nosebleed if Chen does anything exceptionally cute.