Quasiperiodic Patterns of the Complex Dimensions of Nonlattice Self-Similar Strings, via the LLL Algorithm

نویسندگان

چکیده

The Lattice String Approximation algorithm (or LSA algorithm) of M. L. Lapidus and van Frankenhuijsen is a procedure that approximates the complex dimensions nonlattice self-similar fractal string by lattice string. implication this set has quasiperiodic pattern. Using algorithm, together with multiprecision polynomial solver MPSolve which due to D. A. Bini, G. Fiorentino Robol, we give new significantly more powerful presentation patterns sets strings. implementation requires practical method for generating simultaneous Diophantine approximations, in some cases can accomplish continued fraction process. Otherwise, as was suggested Frankenhuijsen, use LLL K. Lenstra, H. W. Lovász.

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ژورنال

عنوان ژورنال: Mathematics

سال: 2021

ISSN: ['2227-7390']

DOI: https://doi.org/10.3390/math9060591