This paper investigates the formation and evolution of large-scale cosmic structures through the Modified Einstein Field Interaction (MEFI) theory. By introducing the concept of the dark field, we simulate its effects on the formation of galaxy clusters, superclusters, cosmic filaments, and cosmic voids. The MEFI theory offers a novel perspective on the clustering of matter and the cosmic web, suggesting a spacetime compression mechanism as an alternative to dark matter. The simulations provide insights into the role of the dark field in shaping the large-scale structure of the universe. Python code for each simulation is included.