Wave interference is a phenomenon most notably demonstrated by Thomas Young’s double-slit experiment in 1801, in which two combining wave sources produced a distinguishable interference pattern. Further studies by Nye and Berry in 1974 explored the resulting interference patterns and dislocations created when combining multiple optical waves. One particular dislocation they studied was an optical vortex: a singularity in a two-dimensional optical field where the phase of the wave at that point takes on all possible values, thus appearing as a point of destructive interference. These vortices are noted in optical fields, seen in all plane wave interference patterns of three or more interacting waves, and are manipulated in laboratory settings for experimental applications. For instance, vortices may be used to trap and move charged particles in optical tweezers, and vortices are a key component in stimulated emission depletion (STED) microscopy. In this study, plane waves of randomized parameters including phase and amplitude are combined to create interference patterns in one and two dimensions. Using the software Mathematica, the interference patterns are simulated and graphed to identify the presence of vortices, and their corresponding distribution in space is analyzed. The aim of this simulation is to delve into the properties and characteristics of the wave-nature of light, explaining the physics behind how and why optical vortices occur. As various types of plane waves are seen interfering in numerous natural phenomena, this simulation can give further insight into how one may manipulate them for a wide variety of applications and studies.