Even squeezed down to a single pixel, the animation would still technically be a derivative of the original movie. However, using the movie in such a radically transformative manner would almost certainly be considered fair use (or equivalent in other jurisdictions) and thus not actually infringing on the movie's copyright.
In particular, in the united-states, 17 U.S. Code § 107 defines fair use and sets out the four main criteria to be considered when determining whether a use of a copyrighted work is fair:
In determining whether the use made of a work in any particular case is a fair use the factors to be considered shall include—
- the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
- the nature of the copyrighted work;
- the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
- the effect of the use upon the potential market for or value of the copyrighted work.
Let us consider the hypothetical 1x1 pixel animated GIF version of the Shrek movie — or the less hypothetical movie barcodes mentioned in the comments — with respect to these criteria (and the additional guidance provided by the U.S. Copyright Office regarding them):
Purpose and character of use: Squeezing a movie down to a single blinking pixel is highly transformative and, as such, more likely to be considered fair:
Additionally, “transformative” uses are more likely to be considered fair. Transformative uses are those that add something new, with a further purpose or different character, and do not substitute for the original use of the work.
While in a purely mechanical sense downscaling the video to a single pixel (and removing the audio entirely) adds no new information, the idea of transforming a movie in such a way could certainly be considered something new and creative, and the resulting original work of visual art is certainly substantially different in purpose and character from the movie and cannot possibly substitute for it. Indeed, it is unlikely that a typical person viewing the single animated pixel without additional explanation could even recognize it as being based on a movie, or what movie it was based on.
Nature of the copyrighted work: This factor does not particularly weigh in favor of fair use, as the copyrighted work in this case is a creative work of fiction and visual art rather than, say, a technical manual or a news report.
Amount and substantiality of the portion used: While the entire duration of the movie is used, each frame of the movie is transformed and reduced to a vanishingly small fraction of its size and image content (less than one millionth, assuming the original was in full HD resolution) in a manner that does not permit reconstruction of any recognizable portion of the original movie. Furthermore, the audio part of the movie is omitted entirely.
Effect upon potential market or value: As already noted in the analysis for the first factor above, a blinking pixel cannot possibly be a market substitute for an animated feature film. Thus, this factor weighs heavily in favor of fair use.
With three out of the four points weighing strongly in favor of fair use, it seems likely that at least the 1x1 pixel version of the movie would be found sufficiently transformative and distinct from the original to be considered fair use. And the same would likely be true of, say, a 2x3 pixel version too, or indeed any version with so few pixels that no recognizable image can be seen in them.
What about the 60x60 pixel version mentioned in your question, then? Here, we're getting into somewhat murkier territory.
For one thing, now the original movie is clearly recognizable from the downscaled version. Indeed, it could be argued that the downscaled animation — even with just 60x60 pixels and no sound — remains marginally viewable as a movie, and thus could in some sense substitute for the original movie. Whether anyone would actually want to watch a 90 minute 60x60 pixel GIF animation, even for free, instead of proper movie is certainly doubtful. But one could conceivably come up with some imaginary situation where someone might view the two as potential substitutes.
Furthermore, the very fact that the movie is recognizable from the animation somewhat makes the transformativity argument slightly weaker, or at least not quite as obvious: a single blinking pixel is obviously not a movie, but a low-resolution silent movie still is a movie, even if not a very good one. And, whereas one could easily argue that transforming a movie into a single blinking light is an act of artistic expression that creates a completely new viewing experience entirely unlike watching the movie in a normal way, it seems a bit harder to make that same claim about a "thumbnail" version where the characters and events of the original movie are still perceptible, however crudely.
That said, if the matter were to come before a court, it certainly seems possible that a competent lawyer could successfully argue in favor of even the 60x60 pixel version being fair use. But it also seems possible to me that such an argument might not succeed. And, in practice, a lot could depend on the specific context, manner and purpose for which the downscaled version was exhibited and/or distributed.
(For example, as noted in the comments below, thumbnailing images for preview, in the context of an otherwise legitimate index providing legal access to the original images via hyperlinks, has been held to be fair use in several cases, such as Kelly v. Arriba Soft and Perfect 10 v. Google. Yet it's also obvious that merely scaling down the resolution of an image or a video somewhat does not automatically make an otherwise infringing use fair, e.g. if the intent is to provide a free pirate substitute for the commercially sold original work.)
And, of course, for other jurisdictions all bets are off again. While, in general, sufficient transformation of the original work — at least, as noted in Martin Rosenau's answer, to the point where it's impossible to determine whether copying actually occurred or not — should be a defense against copyright infringement everywhere, the specific manner in which this is codified into law and precedent varies a lot between jurisdictions, as consequently does the threshold of what is considered transformative enough.