Organometal halide perovskites have emerged as potential material systems for resistive memory devices besides their outstanding optical and electrical properties. Although halide-perovskite resistive memory has the advantage of operating with a low voltage and large on/off ratio, random distribution in operation voltage remains a challenge in memory application. This stochastic operation characteristic is due to the random formation of conducting filaments that cause resistance fluctuations in the material. Therefore, it is essential to investigate the formation and dissolution of conducting filaments and their structure. However, direct observation of a nanoscale filamentary structure is often challenging. Moreover, detailed studies of conducting filaments in halide-perovskite materials have rarely been reported. By employing a scaling theory with a fractal structure, this study investigates the geometric structures and dynamics of conducting filaments formed in organometal halide perovskite through current noise analysis. The temperature-dependent electrical properties and current noise demonstrate the role of ion migration in the formation of conducting filaments. The findings could enhance the understanding of the resistive switching phenomena of perovskite resistive memory devices in terms of percolative conducting filaments. Thus, providing a route for achieving a stable memory operation by controlling the relevant structure and dynamics of the switching processes.