Connecticut’s Thimble Islands are an archipelago of 365 isles in Long Island Sound. ( Enigma/Alamy)

With 365 isles in the Thimble Islands — one for every day of the year, as the locals say — surely the Connecticut Shore residents could spare one for a visitor. I mean, does that cormorant really need that entire rock? Can’t he scoot over and share?

Despite the high count, only 25 of the pink granite formations are inhabited. Yet on this archipelago 12 miles southeast of New Haven, the word “inhabited,” like its close friend “island,” is open to interpretation.

The Thimbles don’t discriminate: Any outcropping, even a vegetationally challenged mound submerged during high tide, can join the club. As for the definition of “inhabited”: Most of the owners occupy their “cottages” (another fanciful use of language) during the summer months. For many pages of the calendar, the islands are deserted.

Details: Thimble Islands, Conn.

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But on a warm day with a thin comforter of clouds, winter seemed as far away as the North Fork of Long Island, a dark blur on the horizon. Dinghies carrying dogs and groceries zipped around the water. Children dared each other to jump off the dock into the unknown depths. Beachgoers stretched out on sandy Stony Creek Beach, on the mainland, their faces turned toward the islands, a drizzle of hard cookie dough clumps topped by architectural cherries.

All but two of the islands are private, so you can look but not touch down. The best vantage point is from a seafaring vessel, preferably one with an open top deck and a bar. From May through October, tour boats shove off from Stony Creek Town Dock and trace crazy-eights around the islands.

My family and I boarded the 44-foot Sea Mist, declining an offer from a man with a dangling earring and a bathtub-size boat. (A town worker said that the sightseeing trips follow the same route and the same script.) I carved out a corner on the second level, near a flapping pirate flag and a set of stairs a young crewmember scaled to take our beverage orders.

Capt. Mike Infantino, who controlled the wheel and the microphone, started the tour on the far left side of the timeline: 15,000 years ago, when the Late Wisconsin Glacier receded, leaving behind a giant marble-toss of pink granite and erratics (large, misshapen boulders). In 1614, Dutch explorer Adriaen Block, the Magellan of Long Island Sound, discovered the area, adding the Thimbles to his collection of discoveries.

The islands’ moniker doesn’t derive from the obvious — their sewing-button cuteness — but from the thimbleberry, which once sweetened the banks. The red berry is now rare; after a dedicated search, I finally found it at the Thimbleberry cafe in Stony Creek, but it was in jam form and imported from Michigan.

I’d heard that journalist Jane Pauley and cartoonist Garry Trudeau own a home on one of the islands, but Capt. Mike was not TMZ-ing on the islanders. To protect their privacy, he would not reveal the identities of the 100 families occupying the 95 homes. (One exception: Yale owns Horse Island and uses it as an ecological lab for its Peabody Museum of Natural History.) But he had no qualms about driving in close enough for us to see the tennis court, formal gardens (with well-manicured privets) and English Tudor-style mansion on Rogers Island, the serpent and dolphin statues on West Crib Island and the Malibu Barbie pool that juts 25 feet over the rocks of Davis Island. Nor did he refrain from pointing out the potted palms that the owner stores in a greenhouse on Rogers Island in the winter.

“Why?” he asked. “Because she can.”

During the 45-minute cruise, each island earned its own moment in the spotlight. For example, in the 1800s, Money Island was a self-sufficient community with a post office, a church, a grocery store and a school. Little Pumpkin Island was named after a pumpkin-raising contest and its losing entry. Circus performer Tom Thumb (no joke) visited Cut-in-Two Island for a rendezvous with his love interest; one room of their love nest is allegedly plastered in circus posters. Mother-in-Law Island, meanwhile, memorializes a certain meddlesome family member who followed a pair of newlyweds from their wedding on Money Island to their honeymoon on an adjacent one. The mom fell asleep, and the couple quietly rowed back home. Nearby, Capt. Kidd maintained a hide-out on High Island, which features a hidden cut in the rocks that could easily shield a pirate.

When Capt. Mike passed Outer Island, I saw my chance to create my own story on a Thimble Island.

“A lot of people think of these as private fiefdoms owned by the rich,” said Shaun Roche, a U.S. Fish and Wildlife Service park ranger. “But the American public owns Outer Island.”

In 1995, a New York architect, in memory of her late husband, donated the island to the agency, which incorporated the five-acre parcel into the Stewart B. McKinney National Wildlife Refuge. Two-thirds of the area is cordoned off for the birds; the remainder is open to wingless visitors.

To reach Outer Island, I hailed a water taxi from Stony Creek. From the new dock (Hurricane Irene had blown away the old one), I spotted docent Jim Lockhart, who took a break from painting the solar-powered latrine to show me around.

In a covered wooden structure, he led my gaze to a telescope trained on Faulkner’s Island and the lighthouse, the second-oldest in the state. I could almost reach out and pat its red top. I scanned the land for the endangered roseate terns that nest on the island, but not one traffic-cone-orange foot flashed into view. (To protect their habitat, Faulkner’s is closed except for an annual open house, held this weekend.)

I then followed Jim along a short trail wedged between unruly Japanese knotweed and the Long Island Sound. A few yards away, cormorants dried their wings on a rocky knob that could very well have been Island No. 217. Closer to our feet, a vole disappeared down a hole.

“There’s our only resident mammal,” Jim exclaimed.

The route segues into an observation deck, where a plaque provides a brief history of the island and its former inhabitants, including a 19th-century Yale professor of zoology and a couple who raised goats, rabbits, ducks and chickens on the scruffy island. On the return walk, I passed the architect’s house, now occupied by seasonal island keepers, and peered through the window at stylish white couches and abstract art, a shock of urbanity in an otherwise natural setting.

With a half-hour before my taxi pickup, I had time to scramble among the boulders and sift through the tidal pool. In the Moon Garden, just beyond the unofficial Poison Ivy Garden, a stone wall with a round cutout captured the vast landscape in its infinity circle.

The taxi arrived on time, but before we could return to the mainland, we had to drop off a child and her father on High Island. As the boat idled, I was tempted to hop out, but I couldn’t get too greedy. I didn’t need two Thimble Islands.

Details: Thimble Islands, Conn.