The susceptibility of protostellar disks to gravitational instability and subsequent formation of protoplanetary clumps is currently under debate. We perform numerical simulations of the gravitational cloud core collapse until approximately 99% of the initial cloud core mass is accreted by the central protostar and protostellar disk system. We find that the protostellar disk is gravitationally unstable, even in the later phase of negligible mass infall from the surrounding envelope, and quickly develops a flocculent spiral structure. The spiral structure is sharp in the early phase of disk evolution and is diffuse in the later phase. In the early phase when the mass infall from the envelope is sufficiently high, dense protoplanetary clumps form within the spiral arms. Some of the clumps get dispersed during several orbital periods and the others are driven onto the protostar. These episodes of clump infall can increase the luminosity of the protostar by several orders of magnitude. The results are accepted for publication in Astrophysical Journal Letters. This research was done in collaboration with Prof. Shantanu Basu.