Aperiodic

An irrational number stays aperiodic (with an infinite number of non-repeating digits) in all integral bases.

Around the same time Robert Ammann created a set of aperiodic tiles that produced eightfold symmetry.

As further aperiodic sets of tiles were discovered, sets with fewer and fewer shapes were found.

Assuming that the matrix W is a primitive matrix ( irreducible and aperiodic ), then after very many generations only the eigenvector with the largest eigenvalue will prevail, and it is this quasispecies that will eventually dominate.

DNA was later discovered, and, although not crystalline, it possesses properties predicted by Schrödinger—it is a regular but aperiodic molecule.

Inharmonic form Additive synthesis can also produce inharmonic sounds (which are aperiodic waveforms) in which the individual overtones need not have frequencies that are integer multiples of some common fundamental frequency.

In order that the quasicrystal itself be aperiodic, this slice must avoid any lattice plane of the higher-dimensional lattice.

That is, the existence of a single-tile (monohedral) aperiodic prototile set is an open problem.

The aperiodic structures obtained by the cut-and-project method are made diffractive by choosing a suitable orientation for the construction; this is a geometric approach that has also a great appeal for physicists.

The concept of aperiodic crystal was coined by Erwin Schrödinger in another context with a somewhat different meaning.

These are the same methods that produce aperiodic tilings with the additional constraint for the diffractive property.

The Socolar-Taylor tile forms two-dimensional aperiodic tilings, but is defined by combinatorial matching conditions rather than purely by its shape.