  In this paper, we propose an evolving Sierpinski gasket, based on which we
establish a model of evolutionary Sierpinski networks (ESNs) that unifies
deterministic Sierpinski network [Eur. Phys. J. B {\bf 60}, 259 (2007)] and
random Sierpinski network [Eur. Phys. J. B {\bf 65}, 141 (2008)] to the same
framework. We suggest an iterative algorithm generating the ESNs. On the basis
of the algorithm, some relevant properties of presented networks are calculated
or predicted analytically. Analytical solution shows that the networks under
consideration follow a power-law degree distribution, with the distribution
exponent continuously tuned in a wide range. The obtained accurate expression
of clustering coefficient, together with the prediction of average path length
reveals that the ESNs possess small-world effect. All our theoretical results
are successfully contrasted by numerical simulations. Moreover, the
evolutionary prisoner's dilemma game is also studied on some limitations of the
ESNs, i.e., deterministic Sierpinski network and random Sierpinski network.
