  The light curves observed in microlensing events due to binary lenses span an
extremely wide variety of forms, characterised by U-shaped caustic crossings
and/or additional smoother peaks. However, all peaks of the binary-lens light
curve can be traced back to features of caustics of the lens system. Moreover,
all peaks can be categorised as one of only four types (cusp-grazing,
cusp-crossing, fold-crossing or fold-grazing). This enables us to present the
first complete map of the parameter space of the equal-mass case by identifying
regions in which light curves feature the same number and nature of peaks. We
find that the total number of morphologies that can be obtained is 73 out of
232 different regions. The partition of the parameter space so-obtained
provides a new key to optimise modelling of observed events through a clever
choice of initial conditions for fitting algorithms.
