Alcatraz TV Show Fans Seek Out Secret Room

National Parks Service rep Alexandra Picavet tells TMZ ... tourists are starting to stray from their tours and sneak into "closed areas" on the former federal prison.

Picavet says many of the not-so-super sleuths have confessed they're looking for a high tech control room ... described on the show as a "bat-cave underneath Alcatraz."

Picavet says they've now posted the following sign on the island: "The TV show Alcatraz is fictional, many areas it depicts are not real. Closed areas protect you, historic structures and nesting birds."