  Discrete-time quantum walks can be regarded as quantum dynamical simulators
since they can simulate spatially discretized Schr\"{o}dinger, massive Dirac,
and Klein-Gordon equations. Here, two different types of Fibonacci
discrete-time quantum walks are studied analytically. The first is the
Fibonacci coin sequence with a generalized Hadamard coin and demonstrates
six-step periodic dynamics. The other model is assumed to have three- or
six-step periodic dynamics with the Fibonacci sequence. We analytically show
that these models have ballistic transportation properties and continuous
limits identical to those of the massless Dirac equation with coin basis
change.
