  We define the epsilon-distortion complexity of a set as the shortest program,
running on a universal Turing machine, which produces this set at the precision
epsilon in the sense of Hausdorff distance. Then, we estimate the
epsilon-distortion complexity of various central Cantor sets on the line
generated by iterated function systems (IFS's). In particular, the
epsilon-distortion complexity of a C^k Cantor set depends, in general, on k and
on its box counting dimension, contrarily to Cantor sets generated by
polynomial IFS or random affine Cantor sets.
