Is it continued_fraction_quadratic you're opposed to, or continued_fraction_periodic_iterator?  The former does not do the same thing as continued_fraction_iterator; it is the inverse of continued_fraction_periodic.  The difference between the latter and continued_fraction_iterator is that continued_fraction_periodic_iterator can take the output of continued_fraction_periodic and produce an iterator that behaves just like such a continued fraction should behave, producing an infinite generator.  So `continued_fraction_periodic_iterator([1, 2, [3]])` makes a generator that yields 1, 2, 3, 3, 3, 3, 3, ....  This can't be imitated with continued_fraction_iterator alone.

(or is it the name you don't like?  I don't really blame you.)

I'll take it out if people would rather not have it, just thought it could be useful, maybe for making convergents to a periodic continued fraction.