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When I think of anthology films, I first think of the various popular horror anthology films, especially those of the 1960s and 1970s. These would include Dr. Teror's House of Horrors, Tales from the Crypt, The House That Dripped Blood, Asylum, etc. These are usually films where seemingly-unconnected characters lives intersect due to their being in the same location at different times or being in the presence of one other character who usually reveals or learns of their fates. These lone "controlling" characters could be a fortune teller, a doctor, a detective or even a crypt keeper. The individual stories are not connected through the characters but through thematic outcomes.
There are also some horror films which involve a character seeking revenge on others and we see how this is accomplished usually through some kind of "poetic justice". Vincent Price's The Abominable Dr. Phibes and Theater of Blood are examples of these straightforward, non-anthology films.
There is another type of anthology called the omnibus which is usually connected by the stories being based on the works of the same author. Examples would include the aforementioned O. Henry's Full House, two Somerset Maugham collections called Trio and Quartet, and Truman Capote's Trilogy.
As far as answering the original question about the specific storytelling device or method's name, I'm unsure of what that is, but I think we've determined that it was developed before the invention of cinema. I don't believe the phrases "interlocking stories" or "episodic narrative" are technical terms, and anyway, they seem to mean different things to different people.
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Last edited by mark f; 04-01-11 at 04:38 AM.