Chapter 8: Implications for Everyday Systems

Section 2: The Growth of Crystals


In some special materials it was discovered in 1984 that atoms are arranged not on a purely repetitive grid, but instead in a pattern with the nested type of structure discussed on page 932. A characteristic feature of such patterns is that they can have approximate pentagonal or icosahedral symmetry, which is impossible for purely repetitive patterns. It has usually been assumed that the arrangement of atoms in a quasicrystal is determined by satisfying a constraint analogous to minimization of energy. And as we saw on page 932 it is indeed possible to get nested patterns by requiring that certain constraints be satisfied. But another explanation for such patterns is that they are the result of growth processes that are some kind of cross between those on pages 373 and 659.

From Stephen Wolfram: A New Kind of Science [citation]