  The presence of log-periodic structures before and after stock market crashes
is considered to be an imprint of an intrinsic discrete scale invariance (DSI)
in this complex system. The fractal framework of the theory leaves open the
possibility of observing self-similar log-periodic structures at different time
scales. In the present work we analyze the daily closures of three of the most
important indices worldwide since 2000: the DAX for Germany and the Nasdaq100
and the S&P500 for the United States. The qualitative behaviour of these
different markets is similar during the temporal frame studied. Evidence is
found for decelerating log-periodic oscillations of duration about two years
and starting in September 2000. Moreover, a nested sub-structure starting in
May 2002 is revealed, bringing more evidence to support the hypothesis of
self-similar, log-periodic behavior. Ongoing log-periodic oscillations are also
revealed. A Lomb analysis over the aforementioned periods indicates a
preferential scaling factor $\lambda \sim 2$. Higher order harmonics are also
present. The spectral pattern of the data has been found to be similar to that
of a Weierstrass-type function, used as a prototype of a log-periodic fractal
function.
