  Topological effects exist from a macroscopic system such as the universe to a
microscopic system described by quantum mechanics. We show here that an
interesting geometric structure can be created by the self replication
procedure of a square with an enclosed circle, in which the sum of the circles
area will remain the same but the sum of the circumference will increase. It is
demonstrated by means of Monte Carlo simulations that these topological
features have great impacts to the vacuum pumping probability and the photon
absorption probability of the active surface. The results show significant
improvement of the system performance and have application potential in vacuum
pumping of large research facilities such as a nuclear fusion reactor,
synchrotron and in photovoltaic industry.
