A few miles away, Dr. Sutton made owning his own island sound more like the movie “The Money Pit” or the sitcom “Bless This Mess” than something relaxing and idyllic. He said he put money into necessities, like a decommissioned Navy vessel to get to his island and a barge that can carry about one tractor-trailer load of material from the mainland.

He also said he has had enough. He put the two islands on the market in May for $13 million.

“You know, I started in my 70s. Now I’m 85. I’m less adventurous,” Dr. Sutton said. “It’s not about me or my wishes or dreams any more. I can dream in a chair.”

Originally, his dreams did not include the larger Pea Island close by, but when it became available in 2015, he bought it as a safeguard. “It protects whoever is going to own this from having a hostile neighbor or anything like that,” he said, referring to Columbia Island.

There is nothing on Pea Island but trees and grass, and at about four acres, it is more than twice the size of Columbia Island. Exactly how large Columbia Island is depends on when measurements are taken. It grows and shrinks with the tide. A small sandy beach beyond the 14-foot sea wall disappears when the tide comes in and reappears, inch by inch, when it goes out.

The one building on Columbia Island was built as the base of a radio transmitter. It once supported a broadcast tower over 400 feet tall for WCBS-AM (whose call letters when the tower went up in the 1940s were WABC-AM). But the station moved to another tower on a different island in Long Island Sound in the 1960s.