Solved: The mathematics of the Hollywood blockbuster - physics-math - 18 February 2010 - New Scientist
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In the 1990s, a team at the University of Texas, Austin, measured the attention spans of volunteers as they performed hundreds of consecutive trials. When they turned these measurements into a series of waves using a mathematical trick called a Fourier transform, the waves increased in magnitude as their frequency decreased.
This property is known as a 1/f fluctuation, or “pink noise”, and in this case it meant that attention spans of particular lengths were recurring at regular intervals. The pioneering chaos theorist Benoit Mandelbrot found that annual flood levels of the Nile follow this pattern; others have observed it in music and air turbulence.
To find out whether the length of camera shots in films might follow 1/f too, Cutting measured the duration of every shot in 150 high-grossing Hollywood movies in various genres released between 1935 and 2005. He then turned these into a series of waves for each film. He found that later films were more likely to obey the 1/f law than earlier ones (Psychological Science, in press). But he stresses that it isn’t just fast-paced action films like Die Hard II that follow 1/f. Rather, the important thing is having shots of similar length that recur in a regular pattern throughout a film.”
