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arXiv · 0705.0895

Epsilon-Distortion Complexity for Cantor Sets

C. Bonanno·J. -R. Chazottes·P. Collet
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Abstract

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.

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C. Bonanno, J. -R. Chazottes, P. Collet. 2007-05-07. Epsilon-Distortion Complexity for Cantor Sets. https://arxiv.org/abs/0705.0895

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