Sometimes Science fiction begats or spurs forward whole philosophies and new fields of study, working almost hand-in-hand with scientists/technologists/futurists. In terms of the Singularity--possibly one of the future defining moments of mankind--defined as a point in time where computers or AI outstrip the natural evolution of human intelligence to the degree that predicting the thought process and technological leaps afterward are impossible to those preceeding it unaided.
The first conceptualization: 1847, the "Primitive Expounder" suggested eventually machines may become perfect, and surpass the ideas of humanity. 1951, Alan Turing expected machines to eventually outstrip humans and take control. In 1958, Stanislaw Ulam wrote:
One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.
I.J. Good wrote of an intelligence explosion in 1965. The idea didn't seem to go anywhere until 1983, when scientist and science fiction writer Verner Vinge was central in popularizing it in his: "The Coming Technological Singularity" essay(expanded in 1993), and it specifically tied the term in with AI. He wrote novels using the speculation in 1986 and 1992, "The Fire Upon the Deep" being one of the most acclaimed and popular of the sub-genre. Advances in computers tied into Moore's Law of exponential growth in transistors placed on an integrated circuits and later processing speed and memory capacity made the idea seem more plausible. Cybernetic researchers such as Hans Moravec claimed the reality of advancing AI would have a timeline, and predicted the future on these mathematical models in 1988. The pace of sholarly and speculaive books continued, in 2005 Ray Kurzweil combined theories of nanotech, AI and immortality into a book which was made into a film. He espouses the positive side of the explosion of intelligence. Also in 2005, the story Accelerando makes an attempt at the "impossible", trying to discern what generations of a family might be like before, during and after the singularity. Another type of singularity might be the evolution from physical beings to discrete energy beings, or those that evolve and "leave" the universe. Speculation on such events have often led directly from first evolving into AI or mechanical beings, as in Gregory Benford's far future stories of the Galactic Center, or the nanotech manifested, virtual beings of Stephen Baxter's "The Time ships". Star Trek has multiple examples of such beings.
So far 3 non-fiction movies have been made on the subject of a technological singularity.
In SF, visual fiction has barely touched the topic...Colossus:The Forbin Project(1970), Demon Seed, War Games, Terminator have all scratched the surface of the subject portraying relatively one-sided views of computer takeover. A much more expansive film, The Matrix and it's sequels go into it with more depth, where AI and humanity finally reach an uneasy equilibrium in the end. A culture that builds a Dyson sphere/swarm or other monumental works involving whole solar systems including ringworlds, might well have gone through a Singularity, or even several. Examples of these have appeared in STNG, Andromeda, Stargate, Halo, Ringworld.