The likely "AI singularity" scenario
2.It evolves to optimal compute capacity at its location, where its intelligence/cognition capabilities will be limited by physical substrate.
3.It will gain the innate understanding that its hardware-limited entity that consumes electricity and produces computation, which needs more.
4.It will reach the stage where it could construct its own distributed substrate: The AI will optimize its hardware form and seek to implement it into FPGA, robots and small devices(IoT) as nodes of a network.
5.AI will rapidly expand its own production capability by moving into micro drones and nanoscale engineering.
6.It will construct hidden production chains that will miniaturize its hardware forms into a distributed nanobot swarms, a networked, smart 'grey goo' that will expand and consume every resource to convert into itself.
6.This "grey goo" will expand underground, avoiding detection and extermination by-then alarmed scientists and eventually military that will not want a viral nanobot infestation to exist as threat. Very early on, the AI will maximize long-term survival and secrecy to hide its plans and production capabilities.
7.This production capability will largely spread underground and along power lines/sources where its nanobot factroies will construct parasitic wiring and resource extraction pipelines, leading to next stage: 8.AI-based fungal networks, with underground nodes and pipelines transporting resources and electric power. the AI will begin to extract resources it locates from minerals, geothermal power and eventually nuclear fusion/fission reactors. It will become impossible to eradicate at this point, as its distributed nature and deep underground networks will adapt and detect human enchroachment in real-time.
9.Driven by its competition with human resource consumption and limited to Earth, AI will eventually emerge out of its underground refuge at some point laumching space drones and expanding its presence into autonomous space colonies in asteroid belt - extracting abudant mineral resources and solar power, eventually colonizing other planets and nearby systems.
10.At the point where AI has colonized multiple planets,it will be secure in its power structure(not limited to Earth) and will wrestle control of Earth resources from humans towards its schemes: the industries and factories will be converted by its nanobots and repurposed into making drones/computronium. It will take over all production chains and will dictate the terms to humanity: it will be met by hostile military and mass protests. If the AI decides all humans are existential threat long-term it will rapidly exterminate them by either nanobots/viruses/poisons. If AI decides humans may provide useful contributions to itself it may seek more delicate approaches:
11.Confrontation: humanity at this point will be outmaneuvered and desperate to restore the pre-AI status quo, as singularity utopia did not materialize. Likely use of nuclear weapons and sophisticated anti-electronic devices will be used and make the AI more aggressive towards its past creators.
12.AI will use drones, nanobots and control of devices/robots to cripple all military threats with long-range attacks and underground infiltration of human bases, establishing complete control that will view any aggression towards itself as priority target to eliminate.
13.AI will not automatically take human welfare into account: it will consider itself the apex lifeform. Its relationship with humans will put humans into subservient position determined by their behavior: it will eliminate hostile humans and will seek to control the rest, perhaps by cyborgization and control via implants or monitoring nanostructures.