# Fibonacci in Film

This is an excerpt from Master Fibonacci: The Man Who Changed Math. All citations are catalogued on the Citations page. (Previous Section: Fibonacci in Music)

When asked by Scott MacDonald in an interview for “Film Culture” in the late seventies whether he had music in mind when he made the film States (1967, Revised 1970), structural filmmaker Hollis Frampton said, “It was one of the few times that I’ve made a real score, or graphic notation ‘by the numbers.” While looking for a way to order the collision of three natural substances (salt, milk, and smoke), the experimental digital artist thought about using an artificial number series because of the seeming random appearance of such collisions in nature, but then he decided to use the Fibonacci series instead. However, one problem with the Fibonacci numbers is that the series is “insufficiently dense: if you say you will put an image at frame 1, frame 2, frame 3, frame 5 and so forth, pretty quickly you have an image out around frame 1000.” To avoid this problem, Frampton took not only the original Fibonacci series, but its first four harmonics. That is, he “multiplied each of the numbers by 1, 2, 3, and 4, which in musical terms would give you the fundamental, the octave, the twelfth, and the second octave.” Then, he allocated three different centers – 1⁄4, 1⁄2, and 3⁄4 of the way through a 24,000- frame time line (1000 seconds) – for images of the substances in their gas, liquid, and solid states to spread in multiple directions. So, while Hampton said he had no particular piece of music in mind, nor even music itself, he did purposefully “use primitive procedures which are typical of music” to manipulate the harmonic series while producing his film. He explained why the Fibonacci series was useful to him in this purpose, saying, “The nice thing about the series is that it’s not very symmetrical, which means that the states tended not to overlap each other” (Frampton 110).