I don’t understand the details either, never needed them. All you need to know is this rule:
When sampling a signal (picture, sound, video, …) your sampling frequency (resolution, FPS, …) needs to be at least twice as high as the highest frequency in the signal, otherwise artifacts (new frequencies, patterns that weren’t present in the original, that is aliasing) may occur.
Actually now I’m kinda confused about the detail of the resolution – from a pure signal point of view to correctly represent a 24x24 image I think you’d need to sample it as 48x48 (as the theorem says), but I think it only applies if you’re thinking in sin/cos representation of the image. With nearest neighbour sampling I think you can safely display 24x24 image as 24x24 pixels (as we usually do), nothing “bad” can happen (such as hitting the zeros in the video you linked). But displaying it e.g. as 16x16 you’ll now have to downscale the 24x24 to 12x12 (by averaging each 4 neighboring pixels into one – this effectively does the blurring, i.e. low-pass filtering) and sample that.
Too much signal theory now, I guess simply do a few experiments and pick what looks best
Weeell I’d be careful about this, deciding which data to drop to keep the result nice can be more difficult than simple extrapolating.