"*If I give you a perfect texture at 1000 x 1000, you should not slavishly resize it to 1024 or 512. You will introduce artifacts.

It boils down to keeping an integer multiple (or fraction) of the original number pixels - this minimizes artifacts. If I give you 2048 and you want to shrink it, by all means use 1024, not 1000. But if I give you 2000, shrink it to 1000, not 1024.* "

I totally agree, except for one small (rare) caveat...

If the original texture is just over one of the magic (512, 1024, 2048 etc.) numbers square (A silly example: a texture that is originally 1100x1100) then there is a very good case for shrinking it down to 1024x1024, unless you really need the detail.

And that reason is that when textures are in memory they are padded out to one of those "magic" numbers ('cos that's the way that computers work). So that 1100x1100 texture actually gets padded out  the next highest "magic" number in memory, in this case to 2048x2048 . No extra detail is added - the extra padding is just "wasted" memory (898,704 bytes of it). The texture still is only 1100x1100, but takes up 2048x2048 bytes. All of those extra bytes just sit around, being moved and manipulated and preventing anything else from using that space.

So, as with everything, think ahead before deciding on texture size...

Cheers,
Diolma