Optimal complexity and fractal limits of self-similar tensegrities

We study the optimal (minimum mass) problem for a prototypical self-similar tensegrity column. By considering both global and local instability, we obtain that mass minimization corresponds to the contemporary attainment of instability at all scales. The optimal tensegrity depends on a dimensionless main physical parameter X0 that decreases as the tensegrity span increases or as the carried load decreases. As we show, the optimal complexity (number of self-similar replication tensegrities) grows as X0 decreases with a fractal-like tensegrity limit. Interestingly, we analytically determine a power law dependence of the optimal mass and complexity on the main parameter X0.