The surface morphology of Ti-Mg supported catalyst and the polyethylene particles are studied using scanning electron microscope(SEM) technology. The results show that either the catalyst's surface or polymer particle's surface is irregular and has fractal characteristics, which can be described by fractal parameter. The more interesting discovery is that the surface fractal dimension values of the polymer particles vary periodically with the polymerization time. We call this phenomenon fractal evolution, which can be divided into the "revolution" stage and the "evolution" stage. And then we present polymerization fractal growing model (PFGM), and successfully describe and/or predict the whole evolving process of the polyethylene particle morphology under the different slurry polymerization (including pre-polymerization) conditions without H-2.