A young man who vanished New Year’s Day from his parents’ home in upstate New York was found Sunday in the District after a set of circumstances and coincidences so unexpected that his mother could only call it a miracle.

The story was first reported by the Associated Press.

Nicholas Simmons, 20, who disappeared from a town near Rochester, N.Y., was photographed in Washington by an Associated Press photographer to illustrate the recent cold snap.

The photo showed people seeking the warmth of a heating grate near the Mall in Washington. It appeared on news Web sites on Saturday and was ultimately posted on a Facebook site set up to help find the young man.

In Greece, N.Y., Simmons’s parents were among those who recognized their son in the photo.

Simmons’s father and other relatives began the 375-mile drive to Washington. They also contacted a Fairfax County couple they knew.

The Fairfax friends, Cindy and Peter Gugino, and their daughter Katie found the place where photographer Jacquelyn Martin had shot the picture. It was a grate outside the Federal Trade Commission’s headquarters, near Sixth Street and Constitution Avenue NW.

On a drizzly, chilly Sunday, they went to the site.

Simmons wasn’t there. The Guginos talked with others who were in the area near the grate and “were told he had slept there the night before,” Cindy Gugino said. They went to search in other locations where people in Washington commonly sleep on the streets. Still, they couldn’t find Simmons. But when they returned to the original site, he was there.

The Guginos remained at Sixth and Constitution, cautiously watching and waiting. They saw D.C. police arrive, Cindy Gugino said. A missing persons report on Simmons had been filed, according to D.C. police spokeswoman Gwendolyn Crump.

Cindy Gugino said police confirmed that the man in the report was the man at the site.

He walked to an ambulance and was taken to a hospital, where his father and brother went after arriving in Washington late Sunday.

“He was reunited with his dad,” Cindy Gugino said. “We were happy to have been part of it.”

“It’s a miracle,” said Simmons’s mother, Michelle, reached at home in New York.

“If anybody doesn’t believe in divine intervention” after that series of events, she said, “they are not breathing.”

There would be time to discuss all that had happened at greater length, she said Sunday night. But for the moment, she said, she was exhausted.