There was a time in my life when I would check the internet for new crop circles every day, not because I was particularly interested in the paranormal, but because I loved the geometry of them. I tried drawing a copy of one once, back before I re-discovered the fun of LEGO.
Several other people have worked on recreating crop circles in LEGO form. It's a bit unconventional, I suppose, but I think it is safe to say that these designs fall into the mosaic category.
The first ones I saw were by Chadwick VonVeederveld (who has his own band with an exciting website that my daughter loves). The first of his "circles" is actually a spiralling square:
The second is a re-creation of the B-side label to his band's first 7" label.
As an aside, there's a video of the non-LEGO version of this design spinning, and it has a trippy 3-D effect.
David Pagano (Paganomation), has a video/animation production studio which specializes in LEGO. He worked on a few different crop circle designs for use in a video made for the LEGO Group in 2011. The video was Red Brick Saga #3 - Alien Conquest, and you can see the final result here. The crop circle in the video (shown about five seconds before the end) turned out to be a very simple design, but another, more elaborate version was created for possible use:
He noted that the original design was meant to look like the Classic Space logo, but that LEGO did not approve it, because they thought it didn't really come across as a crop circle, and wanted just a plain circle instead.
Another cute crop circle was done by Mike T. as a collaboration for a UFO scene with PennLUG.
I guess aliens like mosaics and LEGO.
I've collected several more examples of different crop circle techniques in a gallery on flickr. I wonder how many of them were made by Lino Martins' Dodge A-100 Alien Crop Circle Maker? I don't know, but I'm sure the truth is out there...