Generalised Sierpinski carpets are planar sets that generalise the well-known Sierpinski carpet and are defined by means of sequences of patterns. We study the structure of
the sets at the
th iteration in the construction of the generalised carpet, for
. Subsequently, we show that certain families of patterns provide total disconnectedness
of the resulting generalised carpets. Moreover, analogous results hold even in a more general setting.
Key Words: Fractals, Sierpinski carpet, connectedness, graph.
2000 Mathematics Subject Classification: Primary: 28A80;
Secondary: 54H05, 05C10.
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