Self-similarity of binary quasiperiodic sequences

Arithmetic Self-Similarity of Infinite Sequences

We define the arithmetic self-similarity (AS) of a one-sided infinite sequence σ to be the set of arithmetic subsequences of σ which are a vertical shift of σ. We study the AS of several families of sequences, viz. completely additive sequences, Toeplitz words and Keane’s generalized Morse sequences. We give a complete characterization of the AS of completely additive sequences, and classify th...

Self-replicating Sequences of Binary Numbers

An algorithm is proposed which allows sequences of binary numbers to interact. We introduce a 2-dimensional matrix form of the sequences achieved by a general folding method. Interactions between 1-and 2-dimensional forms of binary sequences generate new sequences, which compete with the original ones due to selection pressure. Starting from random initial populations, replicating and self-repl...

A Comparison of Multi-way Similarity Coefficients for Binary Sequences

The paper compares three formulations of n-way (for groups of size n ≥ 2) similarity coefficients for binary sequences. Properties that the similarity coefficients may have in general, not just for specific data, are discussed, and it is investigated how the different n-way formulations are related. Using the n-way Bennani-Heiser coefficients, the similarity between m sequences (2 ≤ m ≤ n) is a...

Characterizing self-similarity in bacteria DNA sequences

Self-similarity and novel sample-length-dependence of conductance in quasiperiodic lateral magnetic superlattices

We study the transport of electrons in a Fibonacci magnetic superlattice produced on a two-dimensional electron gas modulated by parallel magnetic field stripes arranged in a Fibonacci sequence. Both the transmission coefficient and conductance exhibit self-similarity and the six-circle property. The presence of extended states yields a finite conductivity at infinite length, that may be detect...