  Considering gravitational collapse of matter, it is important problem to
clarify what kind of conditions leads to the formation of naked singularity.
For this purpose, we apply the 1+3 orthonormal frame formalism introduced by
Uggla \textit{et al.} to spherically symmetric gravitational collapse of
perfect fluid. This formalism allows us to construct an autonomous system of
evolution and constraint equations for scale-invariant dynamical variables
normalized by the volume expansion rate of the timelike orthonormal frame
vector. We investigate the asymptotic evolution of such dynamical variables
towards the formation of a central singularity and present a conjecture that
the steep spatial gradient for the normalized density function is a
characteristic of the naked singularity formation.
