John tried to face the detectives and tried to take photos of them in Se7en movie.
What is the reason?
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However, it's not unknown, at least in movies, for serial killers to get close to, or insert themselves into the investigation.
Here John Doe disguises himself as a press photographer, perhaps to see how the police are carrying out the investigation....or perhaps because he needed a disguise to exit the building where the Sloth victim was being held.
Also, using the flash makes it harder for the detectives to get a good look at his face.
In fact, the script offers more clues in that it was intended to show that John Doe was following the investigation. Only the final part seems to have made it into the movie...
On the walls, more pictures: of the crime scenes, but from the outside looking in. Long shots. Police cars. Ambulances. Uniformed officers putting up police barrier ribbons outside buildings. The coroner's wagon. Somerset stares at them, taking them in, realizing... MILLS We had him and we let him go. In the backgrounds of the pictures: Somerset and Mills. In another: Mills crossing the street. In another: Somerset and Mills getting out of Somerset's car. One photo, close shot, shows Mills and Somerset on the stairwell of the building where Victor's body was found. It is the picture taken by the balding, almost silly looking reporter.