Series summation of fractal fluctuations in electron billiard arrays

We fabricate a single billiard, a double billiard array, and a triple billiard array by etching a GaInAs/InP heterostructure, and perform a fractal analysis of the low-temperature magneto-conductance fluctuations measured in the billiards to facilitate an empirical study of how fractals combine in a physical system. We compare our results to simulated fractal traces, and find for both experiment and simulation that fluctuations of similar fractal dimension combine to form fluctuations of the same fractal dimension.