What is the least JPG-compressible pattern? (camera shooting piece of cloth, scale/angle/lighting may vary)
Noise is quite good (hard to compress), but it becomes grey when looking from far, becoming easy to compress. A good pattern would be kind of fractal, looking similar at all scales.


Well, there is fractal noise.  I think Brownian noise is fractal, looking the same as you zoom into it.  Wikipedia talks about adding Perlin noise to itself at different scales to produce fractal noise, which is maybe identical, I'm not sure:



I don't think this would be hard to compress, though.  Noise is hard for lossless compression, but JPEG is lossy, so it's just going to throw away the detail instead of struggling with it.  I'm not sure if it's possible to make something "hard for JPEG to compress" since it will just ignore anything that's too hard to compress at that quality level.

Something with hard edges at any scale would probably be better, like the infinite checkerboard plane:



Also something with lots of colors.  Maybe look at actual fractals instead of fractal noise.  Maybe a Mondrian fractal?  :)