The two towers of The Atlantic Mills have rounded walls and elegant domes, and they would look just right on a Byzantine church. Built in 1849, this site was once the throbbing heart of Olneyville, and untold thousands toiled in its workrooms. The Mills were the brainchild of Charles Tillinghast James, a Rhode Island senator and an early proponent of steam-powered mills. After a century of continuous operation, the factory closed in 1953. Today, the structure is a weathered husk of its former self. Violent storms and near-abandonment have taken their toll on the Mills’ sprawling brick walls. But numerous businesses are now headquartered here, including artists’ studios, a discount furniture store and an English-language school. The Big Top Flea Market opens its doors in the Mills every weekend, drawing a range of shoppers and small-time vendors. The interior is a labyrinth of corridors and converted offices; the old machinery is long gone, and with its patchy walls and ceilings, renovation seems to be an ongoing process. But the towers are the standouts: Curved staircases wind their way upward, with bannisters that curl like seashells. Tall windows illuminate the expansive floorboards, and the empty alcoves echo with stepping feet. They remain architectural marvels, and in Olneyville, no monument is so iconic.