  The Geroch/Stephani transformation is a solution-generating transformation,
and may generate spiky solutions. The spikes in solutions generated so far are
either early-time permanent spikes or transient spikes. We want to generate a
solution with a late-time permanent spike. We achieve this by applying the
Stephani transformation with the rotational Killing vector field of the locally
rotationally symmetric Jacobs solution. The late-time permanent spike occurs
along the cylindrical axis. The generated solution also features a rich variety
of transient structures. We introduce a new technique to analyse these
structures. Our findings lead us to discover a transient behaviour, which we
call the overshoot transition.
