  Ghost measures of regular sequences---the unbounded analogue of automatic
sequences---are generalisations of standard fractal mass distributions. They
were introduced to determine fractal (or self-similar) properties of regular
sequences similar to those related to automatic sequences. The existence and
continuity of ghost measures for a large class of regular sequences was
recently given by Coons, Evans and Ma\~nibo. In this paper, we provide an
explicit connection between fractals and regular sequences by showing that the
graphs of ghost distributions---the distribution functions of ghost
measures---of the above-mentioned class of regular sequences are sections of
self-affine sets. As an application of our result, we show that the ghost
distributions of the Zaremba sequences---regular sequences of the denominators
of the convergents of badly approximable numbers---are all singular continuous.
