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We create a series of vortex beams consisting of positive and negative topological charges and develop a geometry where they interfere creating azimuthal multiple-beam interference effects. Usually the combination of two beams with opposite charges creates an azimuthal two-beam interference effect where the intensity varies sinusoidally with azimuthal angle. We combine several of these beams to create patterns where the interference becomes more sharply defined in the azimuthal direction and where destructive interference eliminates some of the intensity peaks. The process is complicated by the fact that the radii of the different vortex beams depend on the topological charge and the focal length of the Fourier lens. We generate a series of patterns where the different charges are focused with different focal lengths such that their radii agree. However to encode these, we encode patterns from the lower charges that have been Fresnel diffracted to the plane of the highest charge. These complicated patterns are encoded onto a liquid crystal display (LCD). Experimental results agree well with theory.