Gumbo’s flavor is further influenced by roux, the blend of fat and flour used to thicken the broth. It’s a French technique adopted by Louisianians , who often cook the roux so long that it darkens and takes on bitter notes reminiscent of Mexican mole. Sliced okra and the sassafras powder known as filé, a Native American contribution to Louisiana cooking, are also used as gumbo thickeners, either in combination or in place of roux.

All of which is to say that New Orleans gumbo welcomed considerable variation and interpretation even before chefs and home cooks started to add collard greens and Vietnamese fish sauce to their pots.

The pale-roux gumbo with shrimp, crab and oysters that Billy Thurman, a commercial fisherman, cooks at home in Meraux, a 25-minute drive down the Mississippi River from the French Quarter, has little in common with the inky brown duck-andouille gumbo served at Upperline, a traditional restaurant in Uptown.

“Everybody likes it different,” Mr. Thurman said as he stirred his roux with a rubber spatula.

That a single dish can encompass such a broad spectrum of flavor is a big part of gumbo’s enduring local appeal. “Of all the many dishes in Louisiana cooking, gumbo is the one that most singularly defines us,” said Frank Brigtsen, the chef and an owner of Brigtsen’s Restaurant, where rabbit filé gumbo has been a signature offering for 25 years.

Mr. Brigtsen echoes the sentiments of local chefs who came of age, as he did, in the 1980s and ’90s. In those years, the city’s economy realigned around tourism and the rising national fame of its restaurants and chefs. It would have been unthinkable for a restaurant serving New Orleans food to leave gumbo off its menu.

Emeril Lagasse, arguably the most famous chef to come out of New Orleans, has served gumbo at all of the 18 restaurants he has opened since he started his empire in 1990.