  We present a simple method to efficiently compute a lower limit of the
topological entropy and its spatial distribution for two-dimensional mappings.
These mappings could represent either two-dimensional time-periodic fluid flows
or three-dimensional magnetic fields, which are periodic in one direction. This
method is based on measuring the length of a material line in the flow.
Depending on the nature of the flow, the fluid can be mixed very efficiently
which causes the line to stretch. Here we study a method that adaptively
increases the resolution at locations along the line where folds lead to high
curvature. This reduces the computational cost greatly which allows us to study
unprecedented parameter regimes. We demonstrate how this efficient
implementation allows the computation of the variation of the finite-time
topological entropy in the mapping. This measure quantifies spatial variations
of the braiding efficiency, important in many practical applications.
