It basically is a teaching play about this two-dimensional world. How it functions physically, which teaches about physics. How its society works, which is a satirical parable of our own society, of course. And then there is a little science fiction, mathematics, philosophy and somewhat TRON-ish fantasy.
About half-way into the film a 3D character appears in Flatland. He tries to explain the movie's star, "A Square" (That's his name. He's the brother of "B Square"), that there is a dimension beyond him. But since it is hard to explain the 3rd dimension to "A Square" the 2D character and the audience are transported into the 3rd dimension inhabited by spheres, cubes etc. It happens what has to happen: "A Square" concludes that when there is a dimension beyond his there must also be a dimension beyond the 3rd one. A theory which the 3D character can only laugh at...
The approach is rather comedic, but the film is hardly kids stuff. A noteworthy stylistic decision is the unusual narrative. Instead of a voice-over it constantly switches to intertitles just like in a silent picture. At least during the first half when the audience needs to get a grasp on the basics of the two-dimensional universe. It gives the film an odd pacing but it worked quite well for me, simply because it's a fresh approach. The animation is crude, which becomes especially evident when the film switches into the 3rd dimension (Spaceland). But as simply animated as it might be it was done with a lot of attention to detail and most importantly the world that was created is a consistent and functional one.
It gives a very good understanding of the several dimensions and how it might be if a living entity could exist within only two dimensions. It's comprehensible, but not oversimplified. One purpose of the film, of course, is to make you think about the fourth dimension - what it could be like, the possibilities, and even how certain unexplained phenomena in the world might be explainable with the existence of another dimension. It is a Sci-Fi film that is all about ideas. A welcome departure from the special effects extravaganza that Sci-Fi is usually associated with. More theoretical than most Sci-Fi films, but not as purely theoretical as it might sound from my descriptions. There is plenty of fun to be had as well.
The film is based on a genre-grossing novel written in the 19th century, which you may or may not know. It's said to be popular amongst mathematics, physicists and computer science students. Another adaption of this novel has been made in the same year, a 34-minute short called 'Flatland: The Movie' which appears to be targeted towards a younger audience.
If you find the basic premise even only mildly intriguing then this is a highly recommended watch.
