If police have discovered the motive for the Colorado movie theater rampage, they haven’t revealed it. Motive remains a missing piece of the terrible story of the Aurora massacre.

All such crimes can be described as senseless, or as the manifestation of evil, but what unfolded Friday at the midnight showing of the new Batman movie was something that so far lacks even a madman’s explanation.

Answers may be hidden in the apartment of James Holmes, 24, the suspect in custody. The apartment is booby-trapped, and bomb experts have been engaged in an elaborate set of maneuvers to disarm explosives and incendiary devices linked by tripwires.

Police say the killer at the movie theater had a small arsenal of weapons and a massive amount of ammunition, and he evidently wanted to kill as many innocent people as possible, as dramatically as possible.

Holmes has no criminal history. He has been described by fellow students as quiet, shy and hard to get to know.

He’d been a good student in high school and college — indeed, exceptional, according to University of California at Riverside chancellor Timothy White. He’d graduated from Riverside with highest honors.

But it appears that Holmes was going into a personal tailspin in the months before the shooting. He’d been a doctoral candidate in neuroscience at the University of Colorado at Denver but had performed poorly on comprehensive tests this spring and, according to a faculty source, was in danger of going on academic probation. He had decided to quit the school and was in the process of withdrawing.

No close friend has emerged to describe Holmes’s mental state. His parents have not made public statements.

Holmes left little obvious trace of himself on social media Web sites. Whether he scrubbed his own online presence or simply had little interaction with other people remains unclear.

A law enforcement official late Friday said investigators are looking at a Web page on an adult-dating site, Adult Friend Finder, in which someone who looks very much like Holmes, with bright-orange-dyed hair and the handle “classicjimbo,” sought to meet sex partners. The account appears to have been created recently. Posted at the top of the page is a question: “Will you visit me in prison?”

If the page is authentic, that would be the closest thing to a warning or sign that Holmes was planning a crime. Law enforcement authorities, however, have yet to authenticate the account, and police have warned the news media to be wary of social media sites that may be fraudulent.

New York City Police Commissioner Ray Kelly, a longtime associate of Aurora Police Chief Dan Oates, said Friday that Holmes had dyed his hair red to look like the Joker, the Batman villain, and told police when arrested that he was the Joker. Oates would not confirm Kelly’s account. Witnesses did not describe the gunman as looking like the Joker — who, as Batman fans know, actually has green hair — or saying anything to indicate that he was adopting the persona of the fictional villain.

The picture is likely to become clearer as investigators obtain more information about the suspect, but for the moment, the motive remains speculative, something inferred from the gunman’s actions more than from anything he communicated directly.

“Mass-shooting cases have the common motive of an attacker seeking immortality,” said Michael Welner, a forensic psychiatrist who is chairman of the Forensic Panel in New York. “Mass shootings are invariably, invariably carried out by people who have had high self-esteem. They are people who had high expectations of themselves.”