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Abstract We present a novel methodology to generate mechanical structures based on fractal geometry using the chaos game, which generates self-similar point-sets within a polygon. Using the Voronoi decomposition of these points, we are able to generate groups of self-similar structures that can be related back to their chaos game parameters, namely, the polygonal domain, fractional distance, and number of samples. Our approach explores the use of forward design of generative structures, which in some cases can be easier to use for designing than inverse generative design techniques. To this end, the central hypothesis of our work is that structures generated using the chaos game can generate families of self-similar structures that, while not identical, exhibit similar mechanical behavior in a statistical sense. We present a systematic study of these self-similar structures through modal analysis and tensile loading and demonstrate a preliminary confirmation of our hypothesis.