Editing Modular group (section)

==Dyadic monoid==
One important subset of the modular group is the '''dyadic monoid''', which is the [[monoid]] of all strings of the form {{math|''ST{{isup|n{{sub|1}}}}ST{{isup|n{{sub|2}}}}ST{{isup|n{{sub|3}}}}''...}} for positive integers {{math|''n{{sub|i}}''}}. This monoid occurs naturally in the study of [[fractal curve]]s, and describes  the [[self-similarity]] symmetries of the [[Cantor function]], [[Minkowski's question mark function]], and the [[Koch snowflake]], each being a special case of the general [[de Rham curve]]. The monoid also has higher-dimensional linear representations; for example, the {{math|''N'' {{=}} 3}} representation can be understood to describe the self-symmetry of the [[blancmange curve]].