A quasicrystal metasurface is designed to simultaneously generate holographic images and diffraction patterns by arranging nanostructures in a quasi-periodic array. This metasurface combines the global arrangement of meta-atoms with their local phase and amplitude responses to achieve dual functionality. The quasi-periodic structure enables unique diffraction patterns in the far-field, while phase modulation allows for holographic image reconstruction at predefined distances. The study demonstrates that the quasicrystal arrangement can suppress the zero diffraction order in one polarization channel, enabling holographic images in another. The proposed method uses a modified Gerchberg-Saxton algorithm to generate holograms and design the metasurface, allowing for arbitrary arrangements and phase modulation. The metasurface is fabricated using electron beam lithography on a quartz substrate, with silicon nanofins arranged in a Penrose tiling pattern. The results show that the quasicrystal metasurface can achieve high transmission efficiency and polarization conversion, with applications in holographic display, optical switching, and anti-counterfeiting. The study highlights the potential of quasicrystal metasurfaces for multifunctional devices, offering new possibilities for optical manipulation and advanced applications.A quasicrystal metasurface is designed to simultaneously generate holographic images and diffraction patterns by arranging nanostructures in a quasi-periodic array. This metasurface combines the global arrangement of meta-atoms with their local phase and amplitude responses to achieve dual functionality. The quasi-periodic structure enables unique diffraction patterns in the far-field, while phase modulation allows for holographic image reconstruction at predefined distances. The study demonstrates that the quasicrystal arrangement can suppress the zero diffraction order in one polarization channel, enabling holographic images in another. The proposed method uses a modified Gerchberg-Saxton algorithm to generate holograms and design the metasurface, allowing for arbitrary arrangements and phase modulation. The metasurface is fabricated using electron beam lithography on a quartz substrate, with silicon nanofins arranged in a Penrose tiling pattern. The results show that the quasicrystal metasurface can achieve high transmission efficiency and polarization conversion, with applications in holographic display, optical switching, and anti-counterfeiting. The study highlights the potential of quasicrystal metasurfaces for multifunctional devices, offering new possibilities for optical manipulation and advanced applications.