aperiodiset

Aperiodiset is a term that appears in discussions of aperiodicity but is not a standard English technical term. In English-language sources, the adjective is typically aperiodic and the noun form aperiodicity. The form aperiodiset may occur as a non-English or inflected form in other languages, or in informal writing, but it is not widely used in scholarly English.

Aperiodicity refers to the absence of translational repetition. An aperiodic object, such as a tiling or a sequence, does not repeat exactly under any nontrivial translation. In tiling theory, an aperiodic tiling uses a finite set of tile shapes that tile the plane without possessing translational symmetry. The best-known examples are the Penrose tilings and Robinson's aperiodic tile sets; Berger proved the existence of an aperiodic tile set in the 1960s, establishing foundational results.

In one-dimensional sequences, an aperiodic sequence never becomes ultimately periodic; classic examples include the Thue-Morse sequence and other substitution sequences. Aperiodicity also appears in crystallography as long-range order without a conventional periodic lattice, leading to the concept of quasicrystals.

Because of language variation, readers may encounter "aperiodiset" in non-English texts or as an informal form; standard English references will typically use "aperiodic" or "aperiodicity."

See also: aperiodic tiling, Penrose tiling, aperiodic sequence, quasi-crystal, Thue-Morse sequence.