The matter that matters is now called "Quasicrystal" in which the arrangement of atoms follows a definable mathematical pattern, but the pattern is not repeated. There are aspects of this patterning seen in the ancient concept of the "Golden Mean" as well as in medieval Islamic mosaics, which provide for a lot of analogies and pretty language in explaining what this stuff is.
"There can be no such creature" is what Shechtman wrote in his lab notebook when he first observed the patterns that do not repeat themselves using electron diffraction. ... more »