Images of Taylor Swift that had been generated by artificial intelligence and had spread widely across social media in late January probably originated as part of a recurring challenge on one of the internet’s most notorious message boards, according to a new report. Graphika, a research firm that studies disinformation, traced the images back to one community on 4chan, a message board known for sharing hate speech, conspiracy theories and, increasingly, racist and offensive content created using A.I. The people on 4chan who created the images of the singer did so in a sort of game, the researchers said — a test to see whether they could create lewd (and sometimes violent) images of famous female figures. The synthetic Swift images spilled out onto other platforms and were viewed millions of times. Fans rallied to Ms. Swift’s defense, and lawmakers demanded stronger protections against A.I.-created images.