Semiconductor billiards - a controlled environment to study fractals

Fractals describe the scaling properties of a spectacular variety of natura l objects. In general, fractal studies in natural environments are "passive " in the sense that there is no experimental interaction with the system be ing observed. In contrast, in this paper we investigate fractals in an arti ficial environment where controlled changes in the generation process can b e used to study how fractals evolve. To do this we construct micron-sized b illiards in high quality semiconductor materials where the properties of ch aotic electrons can be tuned with precision. By inserting a circle at the c entre of a square billiard, we investigate the transition between two disti nct forms of fractals observed in the billiard's conductance - from exact t o statistical self-affinity.