  We explore the order in chaos by studying the geometric structure of time
series that can be deduced from a visibility mapping. This visibility mapping
associates to each point $(t,x(t))$ of the time series to its horizontal
visibility basin, i.e. the number of points of the time series that can be seen
horizontally from each respective point. We apply this study to the class of
unimodal maps that give rise to equivalent bifurcation diagrams. We use the
classical logistic map to illustrate the main results of this paper: there are
visibility patterns in each cascade of the bifurcation diagram, converging at
the onset of chaos.
  The visibility pattern of a periodic time series is generated from elementary
blocks of visibility in a recursive way. This rule of recurrence applies to all
periodic-doubling cascades. Within a particular window, as the growth parameter
$r$ varies and each period doubles, these blocks are recurrently embedded
forming the visibility pattern for each period. In the limit, at the onset of
chaos, an infinite pattern of visibility appears containing all visibility
patterns of the periodic time series of the cascade.
  We have seen that these visibility patterns have specific properties: (i) the
size of the elementary blocks depends on the period of the time series, (ii)
certain time series sharing the same periodicity can have different elementary
blocks and, therefore, different visibility patterns, (iii) since the 2-period
and 3-period windows are unique, the respective elementary blocks, $ \{2\} $
and $ \{2 \, 3\}$, are also unique and thus, their visibility patterns. We
explore the visibility patterns of other low-periodic time series and also
enumerate all elementary blocks of each of their periodic windows. All of these
visibility patterns are reflected in the corresponding accumulation points at
the onset of chaos, where periodicity is lost.
