4 10 hz amplitude and theta phase modulates gamma 30 50 hz amplitude the main point of these two examples is that the behavior of the smallest scale in the structural hierarchy as in the setae in gecko 39 s feet is transported across scale to provide a robust macroscopic behavior in the largest scale perhaps the most closely related example of structural hierarchy involves spider capture silk its web frame with concentric polygons is a hierarchical structure even though it is much softer the tensile strength per unit weight of capture silk is comparable to that of steel and more importantly capture silk is at least an order of magnitude more extensible than steel in other words the hierarchical structure of the capture silk web frame can extend ten times the size of its relaxed length scale its rupture energy per unit length is 20 times higher than high tensile steel finally this hierarchy structure demonstrates exponential dependence between extension and applied force this unusual logarithmic force extension dependence allows a large dynamic range of its elastic properties with hierarchical structure designs it is possible to amplify the mechanical response of a device and hence reduce motional impedance of the device to an electromechanical or mechanical input while also reducing insertion loss the design approach in the above examples involves one level of amplification from a plurality of first level smaller scale elements to a second level larger scale element these example designs focus on collective modes in which the second level larger element resonates at a frequency determined by the first level smaller elements.