The investment from Mr. Thiel generated a flurry of media attention, but for several years after its founding, the Seasteading Institute did not amount to much. A prototype planned for San Francisco Bay in 2010 never materialized, and seasteading became a punch line to jokes about the techno-utopian fantasies gone awry, even becoming a plotline in the HBO series “Silicon Valley.”

But over the years, the core idea behind seasteading — that a floating city in international waters might give people a chance to redesign society and government — steadily attracted more adherents. In 2011, Mr. Quirk, an author, was at Burning Man when he first heard about seasteading. He was intrigued by the idea and spent the next year learning about the concept.

For Mr. Quirk, Burning Man, where innovators gather, was not just his introduction to seasteading. It was a model for the kind of society that seasteading might enable. “Anyone who goes to Burning Man multiple times become fascinated by the way that rules don’t observe their usual parameters,” he said.

The next year, he was back at Burning Man speaking about seasteading in a geodesic dome. Soon after that, he became involved with the Seasteading Institute, took over as president and, with Mr. Friedman, wrote “Seasteading: How Floating Nations Will Restore The Environment, Enrich The Poor, Cure The Sick and Liberate Humanity From Politicians.”

Seasteading is more than a fanciful hobby to Mr. Quirk and others involved in the effort. It is, in their minds, an opportunity to rewrite the rules that govern society. “Governments just don’t get better,” Mr. Quirk said. “They’re stuck in previous centuries. That’s because land incentivizes a violent monopoly to control it.”

No land, no more conflict, the thinking goes.

Even if the Seasteading Institute is able to start a handful of sustainable structures, there’s no guarantee that a utopian community will flourish. People fight about much more than land, of course, and pirates have emerged as a menace in certain regions. And though maritime law suggests that seasteading may have a sound legal basis, it is impossible to know how real governments might respond to new neighbors floating offshore.

Mr. Quirk and his team are focusing on their Floating Island Project in French Polynesia. The government is creating what is effectively a special economic zone for the Seasteading Institute to experiment in and has offered 100 acres of beachfront where the group can operate.