Large area arrays of vertically-aligned carbon nanotubes (VACNTs) are patterned in a quasi-crystalline Penrose tile arrangement through electron beam lithography definition of Ni catalyst dots and subsequent nanotube growth by plasma-enhanced chemical vapour deposition. When illuminated with a 532nm laser beam high-quality and remarkable diffraction patterns are seen. The diffraction is well matched to theoretical calculations which assume apertures to be present at the location of the VACNTs for transmitted light. The results show that VACNTs act as diffractive elements in reflection and can be used as spatially phased arrays for producing tailored diffraction patterns.