Due to their high ionic conductivity, solid polymer electrolyte (SPE) systems have attracted wide spread attention as the most appropriate choice to fabricate all-solid-state electrochemical devices, namely batteries, sensors and fuel cells. In this work, ion conductive polymer electrolyte membranes have been prepared for battery fabrication. However, fractals were found to grow in these polymer electrolyte membranes weeks after they were prepared. It was believed that the formation of fractal aggregates in these membranes were due to ionic movement. The discovery of fractal growth pattern can be used to understand the effects of such phenomenon in the polymer electrolyte membranes. Digital images of the fractal growth patterns were taken and a simulation model was developed based on the Brownian motion theory and a fractal dialect known as L-system. A computer coding has been designed to simulate and visualize the fractal growth.