There is a lot of talk about 6k resolution from the Epic Dragon by RED, and of course there are 4k TVs now, but I'm wondering what actual film, 35mm particularly has a resolution equivalency of, if it is even possible to do an equivalency. I had read somewhere that it was close to 15k resolution, but I was wondering if this is true.
The closest similarity between film and digital resolution is the comparison of film grain to pixel resolution.
Digital photography does not exhibit film grain, since there is no film for any grain to exist within. In digital cameras, the closest physical equivalents of film grains are the individual elements of the image sensor (e.g. CCD cell), the pixels; just as small-grain film has better resolution than large-grain film, so will an image sensor with more elements result in an image with better resolution.
More grain, means that you get lower resolution, so you can't project the image as big. Less grain means higher resolution.
Film grain or granularity is the random optical texture of processed photographic film due to the presence of small particles of a metallic silver, or dye clouds, developed from silver halide that have received enough photons. While film grain is a function of such particles (or dye clouds) it is not the same thing as such. It is an optical effect, the magnitude of which (amount of grain) depends on both the film stock and the definition at which it is observed. It can be objectionably noticeable in an over-enlarged photographic film photograph. [emphasis added]
The grain of the film is determined partially by the ISO of the film or its "film speed". If you've ever shot still photos with a film camera, you know that you get to choose between different ISOs... most people use 400 because it's middle of the road and allows for both high-light and low-light situations. But, a photographer who knows what they're shooting will often opt for higher or lower ISO. For example, portraiture will use low 50 or 100 ISO film while in dark situations (in a poorly-lit space) will use high, 800-3200 ISO.
Relatively insensitive film, with a correspondingly lower speed index, requires more exposure to light to produce the same image density as a more sensitive film, and is thus commonly termed a slow film. Highly sensitive films are correspondingly termed fast films. In both digital and film photography, the reduction of exposure corresponding to use of higher sensitivities generally leads to reduced image quality (via coarser film grain or higher image noise of other types). In short, the higher the sensitivity, the grainier the image will be. Ultimately sensitivity is limited by the quantum efficiency of the film or sensor. [emphasis added]
But, grain is random while pixels are in straight lines. If you continue reading in the film grain Wikipedia article you read:
However, unlike pixels, film grain does not represent the limit of resolution. As film grains are randomly distributed and have size variation, while image sensor cells are of same size and are arranged in a grid, direct comparison of film and digital resolutions is not straightforward.
In general, as the pixels from a digital image sensor are set in straight lines, they irritate the eye of the viewer more than the randomly arranged film grains. Most people will reject an enlargement that show pixels, whereas a grained film enlargement with lower resolution will be acceptable, and perceived as 'sharper'.
So, because of the random quality of grain, some viewers will accept a lower resolution in film as "better" over a higher resolution enlargement of a digital image... which seems to imply that it is, to some degree, subjective.
So, how does this relate to films? Film stock for moving images also comes in a variety of ISO options. Kodak currently sells camera stock in the following speeds: 50, 200, 250 and 500. So, the "resolution" of the film will depend on the speed of the stock that the crew, usually the DP with some input from the director, decides to use. So, there's not really one "answer" to your question because each of these different film speeds will have a different resolution... and the effective resolution is, as mentioned above, somewhat subjective because the media are so different.
Additionally, remember that most theaters (in the US, anyway) have switched to digital 4K projection. Distributors want it that way because it's much cheaper. So, in the end, all you're getting at the theater is 4K regardless of how it's shot.
Also remember that there are other non-resolution based benefits of film, like color depth and separations in very dark colors and very white colors that will make the image look "better". More info on this in my answer here.
As film is analog, it has no actual resolution in the same sense as a digital file (as you hint at).
Opinions vary on what the 'equivalency' would be. This discussion on Red forums comes to a semi-concensus that it's equivalent to 'around 4k' when we take into real world conditions.