  We study periodic, quasi-periodic (Thue-Morse, Fibonacci, Period Doubling,
Rudin-Shapiro), fractal (Cantor, generalized Cantor), Kolakoski and random
binary sequences using a tight-binding wire model, where a site is a monomer
(e.g., in DNA, a base pair). We use B-DNA as our prototype system. All
sequences have purines, guanine (G) or adenine (A) on the same strand, i.e.,
our prototype binary alphabet is (G,A). Our aim is to examine the influence of
sequence intricacy and magnitude of parameters on energy structure,
localization and charge transport. We study quantities such as autocorrelation
function, eigenspectra, density of states, Lyapunov exponents, transmission
coefficients and current-voltage curves. We show that the degree of sequence
intricacy and the presence of correlations decisively affect the aforementioned
physical properties. Periodic segments have enhanced transport properties.
Specifically, in homogeneous sequences transport efficiency is maximum. There
are several deterministic aperiodic sequences that can support significant
currents, depending on the Fermi level of the leads. Random sequences is the
less efficient category.
