  A simple hierarchical structure is imposed on the set of Lipschitz functions
on streams (i.e. sequences over a fixed alphabet set) under the standard
metric. We prove that sets of non-expanding and contractive functions are
closed under a certain coiterative construction. The closure property is used
to construct new final stream coalgebras over finite alphabets. For an example,
we show that the 2-adic extension of the Collatz function and certain variants
yield final bitstream coalgebras.
