IMHO, these are actually diffusors, designed to be so from the functional angle rather than the looks.
The first one is a two dimensional version that disperses sound waves both vertically and horizontaly (assuming it is mounted on a wall).
The second one is a 1D version that only disperses horizontally.
The third one is a more complex and ambitious design being two 1D diffusers in one. The first pattern is for lower frequencies and the smaller repeated pattern inside each large cavity is "tuned" to the higher frequencies.
The 1D diffusor is good when you don't want to send waves to the ceiling or floor - for example. One example might be locating this on a rear wall with the side walls treated for reflections. That scenario would diffuse the sound field and redirect part of the rear reflections to the sidewalls for absorbtion or further diffusion. That, of course, is assuming the "grooves" have a vertical orientation.
The 2D version is used - according to my reading - in larger spaces. I've seen such panels placed on walls where the panel takes up only a fraction of the height. There is no reason why it could also be used on a ceiling.
The difractal is an interesting idea that could actually work. I am a bit sceptical about the effectiveness of the high frequency tuned QRDs that are located deep in the wells of the low frequency tuned main QRD. But it could be that high frequencies easily penetrate the low frequency wells.
QRDs and skylines are by definition large and bulky. It is an issue for transportation unless they are sold close to where you live. Otherwise, it is a tedious but easy project to make yourself with minimal woodworking skills.
And a last remark. It has been found that poorly constructed QRDs exhibit absorbtion as well as diffusion. The small open seams (from poor construction) function as helmholz resonators. It is up to an educated constructor to combine both with a bit of knowledge. For example, a small slit on the back cover or shallow wells combined with some rockwool in the back of the construction could double the QRD into a tuned absorber - of unknown effectiveness. But don't take my words literally - this is wide open for experimentation and debate.