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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. 

Abstract We present a novel methodology to generate mechanical structures based on the idea of fractal geometry as described by the chaos game. Chaos game is an iterative method that generates self-similar point-sets in the limiting case within a polygonal domain. By computing Voronoi tessellations on these point-sets, our method generates mechanical structures that adopts the self-similarity of the point-sets resulting in fractal distribution of local stiffness. The motivation behind our approach comes from the observation that a typical generative structural design workflow requires the ability to generate families of structures that possess shared behavioral (e.g. thermal, mechanical, etc.) characteristics making each structure distinct but feasible. However, the generation of the alternatives, almost always, requires solving an inverse structural problem which is both conceptually and computationally challenging. The objective of our work is to develop and investigate a forward-design methodology for generating families of structures that, while not identical, exhibit similar mechanical behavior in a statistical sense. 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. Furthermore, each family is uniquely identifiable from the parameters of the chaos game, namely, the polygonal domain, fractional distance, and number of samples. We present a systematic study of these self-similar structures through modal analysis and demonstrate a preliminary confirmation of our hypothesis.