This story involved an artist creating a series of splodges that turned out to be incredibly addictive. The representation spread like wildfire, being reproduced on cushion covers, the floors of swimming pools etc. It was also represented as a drum pattern. The protagonists wanted to break free of it because it was affecting society too deeply and people were getting overly entranced. There may have been the idea of creating a counter-pattern to kind of break the spell. I read this story in the eighties, but have a feeling it was somewhat older than that.
"Rump-Titty-Titty-Tum-TAH-Tee", a short story by Fritz Leiber; first published in The Magazine of Fantasy and Science Fiction, May 1958, available at the Internet Archive.
This story involved an artist creating a series of splodges
Simon seized a brush and plunged it deep in the pot of black paint. Usually he used black for a final splatter if he used it at all, but this time he had the impulse to reverse himself.
Of a sudden Tally's wrists lifted high, hands dangling loosely, almost like a marionette's. There was a dramatic pause. Then his hands came down and beat out a phrase on the log, loudly and with great authority.
Simon's wrist snapped and the middle air was full of free-falling paint which hit the canvas in a fast series of splaaAATs which was an exact copy of Tally's phrase.
that turned out to be incredibly addictive. The representation spread like wildfire, being reproduced on cushion covers, the floors of swimming pools etc.
Norman himself, seeking escape in chess, had checkmated his opponent in a blitz game (where each player must move without hesitation) by banging down his pieces in the rump-titty rhythm—and his subconscious mind had timed it, he said, so that the last move came right on the tee; it was a little pawn-move after a big queen-check on the TAH. Lafcadio, turning to cooking, had found himself mixing salad with a rump-titty flourish. (". . . and a madman to mix it, so the old Spanish recipe says," he finished with a despairing giggle.) Lester Phlegius, seeking release from the obsession in the companionship of a lady spiritualist with whom he had been carrying on a strictly Platonic love affair for ten years, found himself enlivening with the rump-titty rhythm the one chaste embrace they permitted themselves to each meeting. Phoebe had torn herself away and slapped him full-arm across the face. What had horrified Lester was that the impact had coincided precisely with the TAH.
The protagonists wanted to break free of it because it was affecting society too deeply and people were getting overly entranced. There may have been the idea of creating a counter-pattern to kind of break the spell.
"Please, Tally," Norman said. "Wherever he is, we must operate on the hope that there is a counterformula or negative symbol—yang to this yin—which he wants, or wanted, to transmit too—something that will stop this flood of madness we have loosed on the world."
The Leiber story is the one you asked about, but here are some others with similar themes.
"The Ultimate Melody" by Arthur C. Clarke; abridged version (lacking White Hart frame) published in If, February 1957, available at the Internet Archive.
"Pie and Punch and You-Know-Whats" by Robert McCloskey.
"Nothing But Gingerbread Left" by Henry Kuttner and C. L. Moore; first published in Astounding Science-Fiction, January 1943, available at the Internet Archive.
"A Literary Nightmare" aka "Punch, Brothers, Punch" by Mark Twain; available at Project Gutenberg.
Addictive patterns, came out in 80's. There were a few of this sort of story that came out at that time, usually with computers involved. Of course the basic compelling pattern idea goes back quite a few more decades. Sounds like user14111 hit question on the head with 60's vintage Fritz Leiber.