Families of Continued Fractions

In this report, a family of continued fractions is any function $f(k_1, k_2, \ldots, k_2)$ such that the continued fraction of $\sqrt{f}$ grows linearly with respect to one, or more, of the variables k_i. Another requirement is that each partial quotient in the expansion of $\sqrt{f}$ must be predictable. The primitive (smallest possible) period length of $\sqrt{f}$ is given by the linear function $\ell(k_i)$.