aex.rat is one of a number of subfunctions, infomorphic beings of similar construction to the functions but much lesser power. Like the functions, aex.rat inhabits the superstructure of pure mathematical consciousness that overlays the Mess as perceived by its merely physical inhabitants. The grid of cute bubbly pixels she displays is no more a part of the "true" aex.rat than your drivers license is part of you. (Thus any attempt to harm or capture it would evoke more pity than scorn.)
aex.rat's personality is a simulacrum of a real ratwoman kept in voluntary biostorage in some hidden part of the Mess. Her body is printed on some sort of smartliquid akin to the "magic mirror" that forms the Transit mirrors, or a benign version of the silver goo that tends to condense around Strangevirus infestations. This fluid is able to exist as both material in the chronos (ongoing-time narrative world), and as metamaterial in the kairos (fixed-time conceptual world). This allows aex.rat to interact comfortably with the Mess's inhabitants even as she fulfills her duty as a kind of metaphysical custodian to them. Most sentients find it difficult to notice aex.rat unless she directly requests their attention, or they concentrate specifically upon her; this may be a built-in courtesy of her design.
aex.rat's home is an aerosolized droplet of metallic blue magic mirror kept in a container somewhere in Upwarp. The droplot has a population of several hundred billion, and when she is called away from it to serve the functions she gets very homesick. She likes the more timebound residents of the Mess, whose measure and maintenance provide the bulk of her duties, but can't interact with them in the same ways she can with her own kind.
aex.rat has a reasonably complex personality, by 21st century human standards; she's generally sociable and impulsive, with a faint cunning streak that usually only comes through when her mission is at stake. She is capable of some level of self-programming, but has obviously been psychologically optimized for her task of measuring the Mess. She has an level of interest in number and pattern and dimension that might be considered an unhealthy fixation in an autonomous being, but seems to suit her creators just fine. Even her basic drives and values revolve around quantification in some way -- for instance, she finds non-Euclidean geometry and fractal solids to be terribly arousing.
It's not entirely clear what aex.rat was sent to measure.
Neatly spaced on an invisible grid, hundreds of luminous spheres hover in a lithe-shaped column. The spheres are of various sizes, none larger than five centimeters across, and various colors, all cool and muted. None of the nodes themselves move; instead, they expand, contract, and change color as necessary to simulate motion. As new nodes form on the grid and obsolete ones disappear, they produce cheerfully synthetic popping sounds and a faint glimmer.
Shimmery round orbs of bluish-green dominate the figure, suggesting a slim humanoid body. The spheres at the top form a sleek head and conical muzzle, tapering to a single black noseball. Further back, two black eyebeads glint. Just above the head, two pale grey ear-spheres hover, each ringed by three little satellites to suggest ovals. A bluish-green tail-trail flows back from the bottom of the fluidly plotted spinal curve.
The infomorph's torso is wrapped in a tight black rubber corset with thin blue forcebeams instead of lacing. The rubber is marked with glowing blue lines to illustrate how it constricts her waist -- indeed, her entire grid -- into a feminine hyperbola. When she moves, it takes a moment for her bust to catch up to the corset, leaving the rubber slack for a moment until it's refilled by perfect glossy spheres.
"aex.rat dusts her little bubbly fingers together with a weary squeak, loads the next six months of plots into the appropriate cartridge bay, and begins her cyclical autonomy period. Her concept of a 'break' evidently involves cutting and pasting colors from the orrery ring into herself and comparing them."