  Gravitational microlensing has proven to be a powerful tool in the study of
quasars, providing some of the strongest limits on the scales of structure in
the central engine. Typically sources are considered to be smoothly varying on
some particular scale; such simple sources result in recognisable time scales
in microlensing light curves from which the size of the source can be
determined. Various emission processes, however, result in sources with a
fractal appearance, possessing structure on a range of scales. Here, the
gravitational microlensing of such fractal sources at the heart of quasars is
considered. It is shown that the resulting light curves reflect the fractal
nature of the sources, possessing pronounced structure at various scales,
markedly different to the case with the random distribution of emission clouds
that are typically considered. Hence, the determination of a characteristic
scale of variability in a microlensing light curve may not necessarily reveal
the size of the individual emission clouds, the key value that is required to
determine the physical state of the emission region, rather it may correspond
to a particular hierarchy in a fractal structure. Current X-ray satellites can
detect such fractal structure via the monitoring of gravitationally lensed
quasars during a microlensing event, providing a test of high energy emission
processes in quasars.
