  We investigate quantum walks which play an important role in the modelling of
many phenomena. The detailed and thorough description is given to the discrete
quantum walks on a line, where the total quantum state consists of quantum
states of the walker and the coin. In addition to the standard walker
probability distribution, we introduce the coin probability distribution which
gives more complete quantum walk description and novel visualization in terms
of the so called polyanders (analogs of trianders in DNA visualization). The
methods of final states computation and the Fourier transform are presented for
the Hadamard quantum walk.
