Canad. J. Math. 62(2010), 543-562
Printed: Jun 2010
This paper answers a question of Broomhead, Montaldi and Sidorov about the existence of gaskets of a particular type related to the Sierpiński sieve. These gaskets are given by iterated function systems that do not satisfy the open set condition. We use the methods of Ngai and Wang to compute the dimension of these gaskets.
28A80 - Fractals [See also 37Fxx]
28A78 - Hausdorff and packing measures
11R06 - PV-numbers and generalizations; other special algebraic numbers; Mahler measure