Identifying elementary iterated systems through algorithmic inference: The Cantor set example

We come back to the old problem of fractal identification within the new framework of algorithmic Inference. The key points are: (i) to identify sufficient statistics to be put in connection with the unknown values of the fractal parameters, and (ii) to manage the timing of the iterated process through spatial statistics. We fill these tasks successfully with the Cantor sets. We are able to compute confidence intervals for both the scaling parameter ϑ and the iteration number n at which we are observing a set. We both check numerically the coverage of these intervals and delineate a general strategy for affording more complex iterated systems.