Geodesic
Two-dimension approximations by the method of dividing toric tilings
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 30, Tome 440 (2015), pp. 81-98

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An infinite sequence of dividing two-dimensional toric tilings is constructed via the differentiation method. The nucleus of these tilings has radius tending to zero and it contains a point having the best approximations on tori with respect to some norm metric which is defined by the initial karyon. 
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     author = {V. G. Zhuravlev},
     title = {Two-dimension approximations by the method of dividing toric tilings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {81--98},
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     volume = {440},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_440_a6/}
}
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V. G. Zhuravlev. Two-dimension approximations by the method of dividing toric tilings. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 30, Tome 440 (2015), pp. 81-98. http://geodesic.mathdoc.fr/item/ZNSL_2015_440_a6/