  We analyze a set of discrete-time quantum walks for which the displacements
on a chain follow binary aperiodic jumps according to three paradigmatic
sequences: Fibonacci, Thue-Morse and Rudin-Shapiro. We use a generalized
Hadamard coin $\widehat C_{H}$ as well as a generalized Fourier coin $\widehat
C_{K}$. We verify the QW experiences a slowdown of the wavepacket spreading ---
$\sigma ^2 (t) \sim t^\alpha $ --- by the aperiodic jumps whose exponent,
$\alpha$, depends on the type of aperiodicity. Additional aperiodicity-induced
effects also emerge, namely: (i) while the superdiffusive regime ($1<\alpha<2$)
is predominant, $\alpha$ displays an unusual sensibility with the type of coin
operator where the more pronounced differences emerge for the Rudin-Shapiro and
random protocol; (ii) even though the angle $\theta$ of the coin operator is
homogeneous in space and time, there is a nonmonotonic dependence of $\alpha$
with $\theta$. Fingerprints of the aperiodicity in the hoppings are also found
when additional distributional measures such as Shannon entropy, IPR,
Jensen-Shannon dissimilarity, and kurtosis are computed. Finally, we argue the
spin-lattice entanglement is enhanced by aperiodic jumps.
