The nuclear matrix associated protein SMAR1 is sensitive to p53 and acts as a stress inducer as well as a regulator in the p53 regulatory network. Depending on the amount of stress SMAR1 stimulates, it can drive the p53 dynamics in the system to various dynamical states which correspond to various cellular states. The behavior of p53 in these dynamical states is found to be multifractal, due to the mostly long range correlations and large scale fluctuations imparted by stress. This fractal behavior is exhibited in the topological properties of the networks constructed from these dynamical states, and is a signature of self-organization to optimize information flow in the dynamics. The assortativity found in these networks is due to perturbation induced by stress, and indicates that the hubs in the time series play a significant role in stress management. SMAR1 can also regulate apoptosis in the presence of HDAC1, depending on the stress induced by it.