Fractals and Chaos in Film

Chaos, and to a lesser extent fractals, have been topics mentioned in some films, and fractals have been used to generate special effects, and in at least one case, music for a film.
Some films have attempted to employ chaos structurally by demonstrating sensitivity to initial conditions. While this is one ingredient of chaos, alone it is not enough to establish the presence of chaos in the mathematical sense.
 
Fractals have been used to analyze film structure in at least two ways.
Olaf Schneider used driven IFS to analyze shot distance and duration of the film Pulp Fiction,
James Cutting and his students investigated 1/f characteristics of shot durations for 150 films from 1935 to 2005.
 
A film could be fractal in a more straightforward geometric sense. For example, the entire film could exhibit some pattern of actions or ideas or structures. Then each act of the film could exhibit a similar pattern, on a scale smaller in some sense. On a still smaller scale, each sequence could exhibit a similar pattern. On an even smaller scale, each scene could exhibit a similar pattern.
Probably the scene is the lower limit of fractality: reproducing this pattern in a single shot or frame seems daunting.
A limited example of this sense of fractal structure was given by Ethan Robinson in his review of the 1986 film The Scene of the Crime.
We have not found an example of a film exhibiting such structure, but alas we have seen only a tiny fraction of all films. Perhaps a better-informed reader can make a suggestion.