The design of stealthy hyperuniform (SHU) materials has been a critical topic in realizing bandgap materials without crystalline order. Most previous approaches to constructing SHU materials, such as the collective coordinate method, have assumed the closed system, maintaining the number of particles inside a system during the design process. Here, I develop the concept of evolving wave networks, allowing for the open-system design of disordered materials based on the evolution process. The programs are applied to introduce the concept of evolving wave networks (Code_Set_Fig_2), classify material states according to network parameters (Code_Set_Fig_3), generate the stealthy hyperuniformity (SHU) shielding of existing materials (Code_Set_Fig_4), and realize preferential attachment in evolving wave networks (Code_Set_Fig_5).