  It is shown how to endow a hierarchy of sets of binary patterns with the
structure of an abstract,normed C*-algebra. In the course we also recover an
intermediate connection with the words of a Dyck language and Tempereley-Lieb
algebras for which we also find that an effective arithmetic code is possible
albeit of greater complexity. We also discuss possible applications associated
with signal theory and waveform engineering on possible ways to embed discrete
computational structures in an analog continuum substrate.
