You pressed the button, it's owned by you, all rights are reserved by default.
> But copyright law only protects “the fruits of intellectual labor” that “are founded in the creative powers of the [human] mind.” COMPENDIUM (THIRD) § 306 (quoting Trade-Mark Cases, 100 U.S. 82, 94 (1879)); see also COMPENDIUM (THIRD) § 313.2 (the Office will not register works “produced by a machine or mere mechanical process” that operates “without any creative input or intervention from a human author” because, under the statute, “a work must be created by a human being”). So Thaler must either provide evidence that the Work is the product of human authorship or convince the Office to depart from a century of copyright jurisprudence.
[0] https://www.copyright.gov/rulings-filings/review-board/docs/...
If you give the computer the instructions, such as “avocado chair”, the avocado chair is yours.
It wouldn’t be yours if it was something like a deep dream- if you ran the program with no input and generated a “random” work.
The report I’ve cited makes a compelling argument against your claim, and several prominent organization’s copyright policies align with it.
Just hitting a "Generate random artwork" button indeed certainly doesn't seem to qualify as "creative output or intervention", but as for how DALL-E and consorts currently work, I'd say that coming up with a suitable prompt text, potentially refining it to get the output closer to what you want, curating the output, maybe using one of the output pictures as input for further processing, etc. arguably all are at least some amount "creative input or intervention from a human author".