In this paper we describe a fractal assembly of copper nanoparticles on different substrates by controlling the chemical replacement reaction. Through calculation, we found that the 'fractal dimensions' of copper dendrites synthesized by us were about 1.832, which agreed well with the 'fractal dimensions' of natural fern leaves (fractal dimension, 1.826), suggesting that the fern fractal model was useful to describe the self-assembly of our copper nanoparticles during the chemical replacement reaction process. These results will be beneficial for the understanding of the role that highly nonequilibrium conditions play in the formation of fractal clusters as well as the self-assembly mystique of metallic nanoparticles in nonequilibrium conditions and also helpful in the future assembly of complicated nanoarchitectures of metallic nanoparticles for potential applications.