The Logrus is an underground cavern located at the exact opposite end of the universe from Amber, by definition. It appears to move around, but actually, it's moving everything ELSE around. As it wanders, it is usually to be found in House Gainax. Its configuration constantly changes.
One must possess shapeshifting to the point of being able to assume primal form in order to sucessfully walk the Logrus from beginning to end. Those who do so, gain the ability to call upon the Logrus to perform various tasks, gaining power over Shadow.
While the TAMD/UNS Pattern has yet to show any direct sentience of its own, the Logrus has been known to manifest an ever-changing squiggle known as the Sign of the Logrus, though which it communicates.
Because it represents change, the Sign of the Logrus is not the most stable of beings. Because the TAMD/UNS Logrus is in some way a manfestation of a greater Logrus, it isn't even always aware of exactly what universe it is in or who it is talking to.
It seems to especially dislike Gabrielle, for reasons which remain unclear... though this dislike has recent transmuted to outright hate, given the results of the Gabrielle / Logrus steel cage grudge match. The reason for this is rather simple...
Apparently jealous of the Serpent for having taken a Bride in Motoko, the Logrus recently took Jacqueline on a date, assuming the form of an attractively waifish woman in order to do so. However, after Jacqui began relationships with Thoric and Mutsumi, she then broke up with the Logrus. This did not put the Logrus in the best of moods when Gabrielle used the form of Jacqueline to distract the Logrus long enough to get in a blast with the Jewel of Judgement, stomping on its heart with cleats in the process.
For a time, the Logrus was plotting the destruction of Ember by whatever means necessary, so as to wipe Gabrielle out of existence. After a co-operative venture with Gabrielle, however, the Logrus seems to have renounced this goal.
The Logrus recently gave birth to a daughter, Jewel, and seems to have turned very 50s sitcom wifey in response to this. This has also led to some conflict with Jacqui over the issue of Jacqui's current romantic relationships...
The Sign of the Logrus manifests itself. "GReeTInGs, EArTh CReaTURes."
Justin says, "Please, umm...state your name."
"I aM thE SIGn oF tHe LOGruS."
"Were you present at the events of [Some chaos date]?"
"WHEreEVer LOGrUs USeRs go, I AM."
"Did you witness the aforementioned death of ten knights of Hendrake?"
"DAMn StRaIGht. It'S ALL GaBRIeLLE's FAult."
Justin sweats. Justin says, "In what manner?"
"PUNk ASs PATtern. HeR and THAT biTCh, GidEON. TelLINg ME, whAt to dO!"
Motoko stares at the sign of the Logrus, and winces.
Shizumaru begins to sweat, as do many other Amberites present.
"Are you saying they sent the demon?" Justin asks.
"ANd THey TOok mY dAmN sanDWIch, too!"