  We investigate quantitative aspects of the LEF property for subgroups of the
topological full group $[[ \sigma ]]$ of a two-sided minimal subshift over a
finite alphabet, measured via the LEF growth function. We show that the LEF
growth of $[[ \sigma ]]^{\prime}$ may be bounded from above and below in terms
of the recurrence function and the complexity function of the subshift,
respectively. As an application, we construct groups of previously unseen LEF
growth types, and exhibit a continuum of finitely generated LEF groups which
may be distinguished from one another by their LEF growth.
