I am reletively New to the Elder Scroll Lore, and the Dwemer have really fascinated me. One aspect in particular are the Animunculi and their ability to function completely independent of their Dwemer creators for hundreds of years. After extensive research, I believe I may have a theory of just how exactly these mysterious, and in retrospect frankly haunting contraptions function.
First and foremost, I would like to refer to what the Animunculi drop when they are destroyed, namely in TES V: Skyrim. Reguardless of the player's level, all Animunculi drop the following: (According to the UESP) somekind of dwemer metal, a leveled soul gem, dwemer oil, and sometimes gemstones. The two items which caught my interest were the gemstones and the soul gems.
Now by basic robotic principles, a robot needs four things to function: A physical form with which to perform an action, commands as to how the form is to be moved, a way of receiving these commands, and a way to interpret the commands and move the form accordingly. For the Animunculi, identifying how it satisfies the first requiorment is quite simple: it's form is made out of dwemer metal in either a spider, sphere guard, or Centurion shape. But what about the last three? Surely the commands came origionally from the Dwemer, but how do they continue to function long after their masters' demise? Perhaps their commands are stored internally, or perhaps something within the ruins is still broadcasting a signal...
As for the third requirement, that of receiving commands, I would suggest looking at a spider for a possible example of a solution. Notice in the Syrim version of the spider, it has a small, deep redish looking gem in its cranial region. (this parallels with the gemstone loot). This gem is referenced in Skyrim with Aicantar's Spider. Aicantar's Journal details how he and his uncle had discovered a Spider which was perfectly intact, save for the fact that it was missing the red gem in its cranium. Furthermore, Aicantar was able to recover one of the gems and fashion the Spider Control Rod, which allowed him to control the Spider. Using this information, I postulate that the medium through which the Animunculi receive orders is this gem. Furthermore, I would like to note that the Dynamo Core found in SKyrim Centurions appears to have this same red gemstone inside of it.
Finally, this leaves the question of how are the Animunculi moved. What powers them? For this final question, I suggest looking to the last unaccounted loot: the soul gem. I postulate that the Dwemer would use soul gems to power the Animunculi. Essentually, the Dwemer would capture highly subjective souls and then put them in the Animunculi, providing the soul with a new, metal body. Just as the control gem would be the brain of the Animunculi, the soul gem would be it's heart. This would also explain the Dwemer's subjugation of the Falmer who, despite being a sentient race, have white souls as of TES V. Somehow, the Dwemer were able to change the Falmer's souls and turn them into subjective cattle ready to be harvested to make the Animunculi. This also explains the abundance of Geode veins in Blackreach.
And so that concludes my theory on the workings of the Animunculi. Thank you for your time and consideration.
-RansomPendragon