Modular Group - Dyadic Monoid

One important subset of the modular group is the dyadic monoid, which is the monoid of all strings of the form for positive integers k,m,n,... . This monoid occurs naturally in the study of fractal curves, and describes the self-similarity symmetries of the Cantor function, Minkowski's question mark function, and the Koch curve, each being a special case of the general de Rham curve. The monoid also has higher-dimensional linear representations; for example, the N=3 representation can be understood to describe the self-symmetry of the blancmange curve.