1/f characteristics of shot duration

The presence of 1/f signals in so many fields, and especially in music, looking for the presence of 1/f patterns in film seems natural.

In Attention and the evolution of Holywood film, James Cutting and his students Jordan DeLong and Christine Nothelfer study the distribution of shot durations for 150 films from 1935 to 2005.

Using a combination of automated analysis and visual inspection, each of 150 films, 10 (Les Miserables, Westward Ho, Anna Karenina, A Tale of Two Cities, Captain Blood, The Informer, The 39 Steps, Mutiny on the Bounty, Top Hat, and A Night at the Opera) released in 1935, 10 in 1940, ..., 10 (Madagascar, Chicken Little, Wedding Crahsers, King Kong, Mr. & Mrs. Smith, Star Wars III, Walk the Line, Harry Potter and the Goblet of Fire, The Longest Yard, and Hitch) in 2005. All films studied were of a style that focuses on narrative, reducing awareness of presentation mechanisms.

To facilitate comparisons, the shot length data of each film was converted to the unit normal distribution. That is, shot lengths were compared to the average shot length of the film, and were scaled so the standard deviation of the shot lengths was 1.

Power spectrum calculations revealed revealed a flat component (1/f0), without systematic diffrences over the years, and a 1/fα component, with some evidence that α approaches 1 for films made in later years.

Generally, action films have spectra closest to 1/f (α = 1), but other categories (adventure, comedy, animation, and drama) all have examples with α close to 1. For example, α = 0.90 for The Perfect Storm, α = 0.92 for Pretty Woman, α = 0.95 for Cinderella, and α = 0.93 for The 39 Steps,

Cutting and his students make several observations.

*   Film ratings and power laws are uncorrelated.

*   The movement to power spectra closer to 1/f was not engineered intentionally by filmmakers.

*   This pattern has emerged, perhaps reflecting a drift in filmmaking styles to scalings familiar, though perhaps unconsciously, from nature.

We echo Richard Voss' comment about why 1/f patterns are so common in music: music mimics how the world changes with time. Perhaps filmmakers have discovered the rythms of changes Nature presents provide a familiar superstructure on which to express narrative elements.

Another possible explanation is that attention span appears to follow a 1/f distribution, so shot sequences with this power law increase the visual momentum, the rate of information gathering.

Lacking a general agreement over the source of 1/f signals in other areas, that we have found no clear reason for their appearance in film is understandable. But oh this does suggest another level of film analysis that may prove quite interesting.

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