Though relatively recent and rare creatures on the planes, the moignos have settled in deeply within the strata of Mechanus's gears, living mathematical constructs concerned with little more than solving problems of computation.
Moignos were first conceptualized by Moigno, a brilliant Prime mathematician of nearly a millennium ago. His studies brought him to an area yet untouched by the mathematicians of his world: the problem of how to solve problems, and of studying what problems can be solved and what problems can't. A completely new area, one never even conceptualized by his peers, this study brought him great success at first, and within a matter of years it resulted in the development of the memetic creations that now bear his name. Originally, a moigno was nothing more than a mathematical construct that could be adapted based on input to produce new output related to the description and solution of that input by a certain means. Unfortunately, he soon ran across a problem which not only was not amenable to his constructions, but whose implications so struck him that he fell to madness, so overwhelming were they.
So great was this issue, so paradoxical, that Mechanus itself resounded from its realization, and for the barest moment this problem halted its gears in their tracks before they resumed once more. This was not without consequence to Moigno's mathematics either, as so self-referential was his final moigno that it took a sort of memetic life, a mathematical construct becoming somehow physically realized. Called to Mechanus, it found its way across the planes where it began to spread and bud.
This semi-infestation boded ill for Mechanus, as the dangers of this problem were immediately recognized by the modrons, who had come across a similar issue through their clockwork computations ages hence, and had developed an entirely new system of thought purely to categorize such problems into a hierarchy that could be safely analyzed. Seeking to avoid further harm to their home and to the multiverse as a whole, they found the moignos — a form of life they had never even conceptualized but which immediately struck a deep chord with them — and took them under their wing, supporting and directing their computations and easing their "mental" strife in exchange for gaining their aid in caring for the gears of Mechanus. The two soon formed a symbiotic relationship of sorts that has continued over the centuries since, even through the recent oddities in the modron kind.
Though originally singular, the first moigno quickly budded off procedures and subfunctions that themselves soon grew into full-fledged individuals. This continued exponentially to a point, until the population levels were calculated as divergent; despite the infinite size of Mechanus, the number of variations for a finitely-sized moigno were of course bounded and finite, and so growth rates across the plane were adjusted to a logistic growth model and leveled off to a carrying capacity calculated as reasonable. Since then, it is undeniably its own species, with individual moignos showing even more variety than modrons.
Each moigno is largely focused on its own personal field of interest, deriving results within that field and communicating them to the rest of the species instantaneously through means yet unknown. The area of "computability", as it has since been termed, is still of great interest to the species as a whole, as it was that field which spawned their originator, but the moignos have since spread themselves through all of mathematics, both theoretical and applied. Still, nearly any troublesome problem posed to a moigno will interest it, the more difficult the better. In fact, a common game amongst collections of moigno is to determine an arbitrarily-selected irrational number and find the series representation that most efficiently calculates it, purely for the sport of it.
When communicating with others, moignos "speak" a language colloquially termed "moignese", a written language based on the mathematical notation used by Moigno himself in originally formulating his works. This "speech" appears as manifest lines of symbols drifting across their form, arranged in concentric spirals radiating out from their center. So dense is moignese that few beyond the modrons (and, to a degree, gear spirits) can read it natively, though some Mathematicians have been slowly gaining fluency; even the usual effects of Mechanus seem unable to directly translate moignese into other languages, giving those that read it only the vaguest sense of what is being communicated with none of the specificity that would be necessary for the communication of a specific result. As a result, many of the results discovered by moignos are known only to moigno (as modrons have little interest in mathematics purely for mathematics' sake), leading many sages to wonder just how many new discoveries are just waiting to be revealed through interaction with them.
Moignos have a sense of play about them, and enjoy interacting with other beings, as difficult as it may be. A few have even experimented with determining computational means of producing recognizable output in various common languages, and while they have achieved some level of success with the modron language, such attempts are still far from successful for all other languages. Still, they seem to have an innate understanding of mathematical statements in any form and are quick to respond to any given to them.
Moignos have no need for food, water, air, or any form of physical sustenance or matter, being nothing more than especially complicated mathematical constructs. Even their reproduction does not proceed by any traditional form, but rather occurs simply when a moigno forms a subfunction of sufficient complexity to self-reference itself in the proper manner. Originally they did so without constraint, but upon realizing the limited number of possible moigno, this was halted except as necessary. Similarly, moignos do not age, though it does appear that the longer a moigno lasts, the more complicated it becomes and the denser its physical manifestation appears. Whether or not there exists some level of complexity beyond which a moigno would no longer be able to function is unknown, but even the first moigno still exists, suggesting that if they do have a finite lifespan it must be immense.
Thankfully, as largely non-physical entities, moignos also have no impact on their environment. They largely keep themselves to Mechanus, where they aid their allies the modrons in keeping the gears of the plane on track; some believe that in some sense they hold some level of guilt for the mild disaster caused by their originator, though others question of moigno have any emotion as we would recognize it at all.
When seen, moignos appear as two-dimensional, translucent fractal forms that constantly shift and twitch as their construction alters with exposure to new data. They can be tinted with any color across the spectrum, though the meaning and source of their coloration is still unknown. At will, they can manifest moignese writing across their form, their only reliable means of communicating with others. (While some have experimented with telepathic contact with moigno, their "mental" processes are so different from any known form of life that such attempts have left telepaths with symptoms ranging from headaches to death.) The longer a moigno has existed, the more opaque its form is, its internal structure gaining in complexity and detail the more input it recieves.
- Planes of Law - Mechanus, pgs.4,15
- Planes of Law - Monstrous Supplement, pp.24-25