%0 Journal Article
%T Epsilon-Distortion Complexity for Cantor Sets
%A C. Bonanno
%A J. -R. Chazottes
%A P. Collet
%J Mathematics
%D 2007
%I arXiv
%X 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.
%U http://arxiv.org/abs/0705.0895v1