Abstract
Let C be the classical Cantor triadic set. For \({\alpha,\beta\in [-1,1]}\) , a sufficient and necessary condition for \({(C\times C)\cap (C\times C+(\alpha,\beta))}\) to be self-similar is obtained.
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Yao, Y., Li, W. Self-similar structure on intersection of Cartesian product of Cantor triadic sets with their translations. Monatsh Math 166, 591–600 (2012). https://doi.org/10.1007/s00605-011-0312-6
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DOI: https://doi.org/10.1007/s00605-011-0312-6