The EU copyright directive from 2003 rules that only a natural person (a human, not a company) can have copyright ownership on its works. Companies only can own perpetual licenses for these works.
Generated art where a machine writes code or produces artwork based on randomization leads to the inventor of the algorithm owning the copyright for it.
As there is nothing like "public domain" in the EU area possible, you can only distance yourself from this work with the CC0 license while stating that you cannot offer any warranty and that you cannot be held responsible for malicious use of the product and that users of the product use it with their own risk.
Source: wrote a code generating engine based on backpropagated ES/HyperNEAT, got sued in front of the EU court because it turned out it got quite good at pentesting, too.
I could offer to talk about it via telegram secure chat, if you're interested. I have the same pseudonym there.
The US Copyright Office says: "The crucial question is “whether the ‘work’ is basically one of human authorship, with the computer [or other device] merely being an assisting instrument, or whether the traditional elements of authorship in the work (literary, artistic, or musical expression or elements of selection, arrangement, etc.) were actually conceived and executed not by man but by a machine.” U.S. Copyright office, Report to the Librarian of Congress by the Register of Copyrights (1966)."
While the dividing line is fuzzy, it is clear that as soon as you're claiming that the art was generated by AI, you are fighting an uphill battle to get a copyright registered.
Again, I am not a lawyer.
Which leads to the conclusion that at least in some cases,a human doing some setup is not enough to grant a copyright.
While this case was partly about the question "can a Monkey own a copyright in a selfie it creates?", I think it got a lot of press because it was so obviously related to the case of AI-created art. If one non-human can get a copyright, why not another? The US Copyright office has shot them both down, on the grounds that only humans can get copyrights.
In the monkey selfie case, the photographer set up the camera, which meant that there were some very abstract settings that involved a human. That wasn't enough to get a copyright. I think at least some hyperparameters would be similar - not really enough to justify creativity.
The U.S. Copyright Office has already declared that if it's generated by a machine, without any creative input or intervention from a human author, then the work is NOT eligible for copyright at all.
They believe that "The copyright law only protects “the fruits of intellectual labor” that “are founded in the creative powers of the mind.” Trade-Mark Cases, 100 U.S. 82, 94 (1879). Because copyright law is limited to “original intellectual conceptions of the author,” the Office will refuse to register a claim if it determines that a human being did not create the work. Burrow-Giles Lithographic Co. v. Sarony, 111 U.S. 53, 58 (1884). ... the Copyright Act protects “original works of authorship.” 17 U.S.C. § 102(a) (emphasis added). To qualify as a work of “authorship” a work must be created by a human being. See Burrow-Giles Lithographic Co., 111 U.S. at 58. Works that do not satisfy this requirement are not copyrightable. The Office will not register works produced by nature, animals, or plants.... Similarly, the Office will not register works produced by a machine or mere mechanical process that operates randomly or automatically without any creative input or intervention from a human author."
I'm quoting chapter 300 here: <https://www.copyright.gov/comp3/chap300/ch300-copyrightable-... of the Compendium of U.S. Copyright Office Practices here <https://www.copyright.gov/comp3/>. The compendium is the "governing administrative manual for registrations and recordations issued by the U.S. Copyright Office." In short, for the US, this is an extremely authoritative source.
A future US court ruling or law change could change this, of course, but I sure wouldn't bet on it. The US Copyright Office has lawyers who specialize in this area, have clearly stated their position, and they are citing specific laws and court cases to justify their position. Also, in most cases you can't go forward with a copyright claim without registration (though you can register after-the-fact); if the US Copyright Office won't allow registration, you'll have a really challenging time even starting a court case.
I'm sure there are edge cases and complications. But the essence is only "unsettled" if you don't look for the existing rulings. A Google search will find actual answers from credible, authoritative sources. Sure, courts and Congress could change it, but it'd require a significant change.
While this information is specific to the U.S., copyright is similar enough in other jurisdictions that there's a decent chance that other jurisdictions would come to the same conclusion. European law in particular has a number of similarities in this area; I'd love to hear from those with more background in other jurisdictions.
Disclaimers: I am not a lawyer, and this is not legal advice.