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Percolation in Random Cantor Sets
Fractals, 1997The d-dimensional random Cantor set is a generalization of the classical "middle-thirds" Cantor set. Starting with the unit cube [0, 1]d, at every stage of the construction we divide each cube remaining into Nd equal subcubes, and select each of these at random with probability p. The resulting limit set is a random fractal C.
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THE SUM OF THE CANTOR SET WITH ITSELF
1993Using ternary representation of the classical Cantor set \(C\subset[0,1]\), the author proves that \(C+C=[0,2]\) and derives a formula for the number of pairs \((x,y)\in C\times C\) for which \(x+y=k\in[0,2]\). The latter result is formulated in terms of the coefficients in the ternary expansion of \(k\).
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A Note on the History of the Cantor Set and Cantor Function
Mathematics Magazine, 1994A search through the primary and secondary literature on Cantor yields little about the history of the Cantor set and Cantor function. In this note, we would like to give some of that history, a sketch of the ideas under consideration at the time of their discovery, and a hypothesis regarding how Cantor came upon them. In particular, Cantor was not the
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The arithmetic decomposition of central Cantor sets
Journal of Mathematical Analysis and Applications, 2018Franciszek Prus-Wiśniowski +1 more
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On Cantor sets and doubling measures
Journal of Mathematical Analysis and Applications, 2012Ville Suomala
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Regular interval Cantor sets of S 1 and minimality
Bulletin of the Brazilian Mathematical Society, 2009Aldo Portela
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