The teenager had become increasingly withdrawn, even from his family. He rarely left his home, a red brick house on a quiet cul-de-sac in the village of Banks, near the west coast of England.

Alone with his thoughts, he scrolled endlessly through online images and descriptions of war, torture and death, feeding an obsession with genocide and killing.

And then, on a bright morning last summer, Axel Rudakubana took a taxi to a children’s dance class in Southport, England. Knife in hand, he rampaged through a crowded room where girls on their summer break had gathered to dance to Taylor Swift and make friendship bracelets. He murdered three of them, and he wounded eight other children and two adults.

In the months since the July 29 attack, the police and prosecutors have worked to retrace the steps leading up to the killing spree, which horrified Britain. They interviewed witnesses, examined hours of CCTV and reviewed thousands of documents, downloads and messages from Mr. Rudakubana’s devices.

On Monday, after Mr. Rudakubana, now 18, pleaded guilty to murder and other charges related to the Southport attack, restrictions on reporting about his case were lifted.

The picture that has emerged, while still limited, is of a deeply troubled individual whose fascination with violence was brought to the authorities’ attention when he was just 13, and who had been known to a number of state agencies for years.