  This paper studies the recursion-theoretic aspects of large-scale geometries
of infinite strings, a subject initiated by Khoussainov and Takisaka (2017). We
investigate several notions of quasi-isometric reductions between recursive
infinite strings and prove various results on the equivalence classes of such
reductions. The main result is the construction of two infinite recursive
strings $\alpha$ and $\beta$ such that $\alpha$ is strictly quasi-isometrically
reducible to $\beta$, but the reduction cannot be made recursive. This answers
an open problem posed by Khoussainov and Takisaka.
