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 theta 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.

Identifying elementary iterated systems through algorithmic inference : The Cantor set example / B. Apolloni, S. Bassis. - In: CHAOS, SOLITONS AND FRACTALS. - ISSN 0960-0779. - 30:1(2006 Oct), pp. 19-29.

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

B. Apolloni
Primo
;
S. Bassis
Ultimo
2006

Abstract

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 theta 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.
Settore INF/01 - Informatica
ott-2006
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/55473
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