A Penrose tiling is an aperiodic tiling consisting of only two tiles and containing five-fold symmetry. The wikipedia entry for Penrose tilings has good images and information about it, plus a couple of photos that help you see how the pattern might look when colored in.
I am aware of the existence of a few small Penrose quilts, but from examining the photos it looks like they contain at most three iterations of the tiling. Not surprising – it’s hard to find images to work from that have more than three iterations. I had to install Inkscape and use the instructions on this page to render out seven iterations of the pattern, but it’s in readiness for when I decide to tackle the pattern.
I have purchased most of the fabric needed to make this quilt, but am not yet ready to start on it. I have a couple of small quilts to finish up before I tackle this one.
Update, November 2015
See http://domesticat.net/2015/11/ends-and-means for how the story of this quilt unfolded, and ended.