Abstract: In order to understand more comprehensively the dynamical mechanism of the multifragmentation taking place in heavy ion collision at intermediate energies, in the present paper, with help of the factorial moment method, we analyze the concrete behaviors of intermittent chaos and fractal in the distributions of the fragments in the reaction final states and the primary fragments formed during the fragmentation process, by simulating some collisions within the framework of the isospin dependent quantum molecular dynamics model. Our results show that 1) the fluctuations of the distribution of these fragments multiplicity are multi-fractal rather than mono-fractal, and 2) the intermittent exponent reaches its maximum at the stage of the multi-fragmentation taking place during the collisions. The universality of these features is verified by studying the similar colliding systems with the same analysis method. These new features we have revealed here not only help us to deepen our understanding of the dynamic mechanism of the multifragmentation, but also enrich our knowledge of nonlinear dynamics.