ε-Distortion Complexity for Cantor Sets
نویسنده
چکیده
We define the ε-distortion complexity of a set as the shortest program, running on a universal Turing machine, which produces this set at the precision ε in the sense of Hausdorff distance. Then, we estimate the ε-distortion complexity of various central Cantor sets on the line generated by iterated function systems (IFS’s). In particular, the ε-distortion complexity of a C 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.
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تاریخ انتشار 2007