I'm looking for a short story or novella about an idyllic, utopian society with a hidden dark side: periodically (every week or month) its inhabitants would descend into madness, violently destroying everything around them and brutally murdering each other. This continued for a day or so, and when it ended, the ordeal was somehow magically undone, with even the dead returning to life. Then everyone would be left with only their memories of the experience, to enjoy their perfect society until the next time around.
The society was some kind of city-state with a vaguely Mediterranean feel, maybe on an island or isolated peninsula. There was a strict rule about visitors, but I can't quite remember what it was: either they had to leave before the violence started unless they agreed to immigrate permanently, or they couldn't leave until they had experienced it at least once.
The story was posted online on what looked like someone's personal website (possibly the author's), split into a separate page for each chapter. I read it sometime in the last several years, and I feel like the writing style reminded me of Jorge Luis Borges.