There is a manga series which is set in this concept of exponential self-replication technology gone wrong somewhere in the past (thus a futuristic dystopia):
https://en.wikipedia.org/wiki/Blame%21
>> The "Netsphere", a sort of computerized control network for The City. The City is an immense volume of artificial structure, separated into massive "floors" by nearly-impenetrable barriers known as "Megastructure". The City is inhabited by scattered human and transhuman tribes as well as hostile cyborgs known as Silicon Creatures. The Net Terminal Genes appear to be the key to halting the unhindered, chaotic expansion of the Megastructure, as well as a way of stopping the murderous robot horde known as the Safeguard from destroying all of humanity.
We'll probably reach technological self-replication singularity before AGI. I envision a small self replicating/repairing/transforming factory that could function based on local resources. Mostly 3d-printers, robots and tools for making tools.
But I think in reality there will be limited resources, energy and pollution we can all use, so we can't have our exponential utopia. Technology will be more like biology, and it will get good at recycling anything.