Ligia L. Cristea and Bertran Steinsky: On totally disconnected generalised Sierpinski carpets, p.27-34

Abstract:

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 $k$th iteration in the construction of the generalised carpet, for $k\ge 1$. 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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