In this work, the Zn-Mg-Cu nanocomposites with different weight percent of Cu were deposited by electrochemical method and their surface and fractal properties were studied. The structural properties of the nanocomposites by X-ray diffraction (XRD) and their morphological properties by atomic force microscopy (AFM) and scanning electron microscopy (SEM) were evaluated. Statistical analysis based on 3D AFM images showed that all synthesized samples exhibit fractal properties and that these properties depend on the type and amount of impurity loaded in the matrix. Also, the results show that the grain size decreases with increasing weight percent of Cu doping. The fractal dimension (Df) of the nanocomposites were measured using the box-counting algorithm between 2 and 3, indicating that Df is independent of the surface scan size and pixel resolution of the images. The results showed that with increasing copper concentration, the fractal dimension and surface roughness decrease and the surface topography becomes more regular. By obtaining the lacunarity coefficient β, it was found that all the nanocomposites have a high degree of surface texture homogeneity with β<0.07 and that the ZM3C4 and ZM3C2 nanocomposites have the lowest and highest lacunarity coefficients compared to the reference nanocomposite ZM3.