241 research outputs found
About the domino problem in the hyperbolic plane, a new solution: complement
In this paper, we complete the construction of paper arXiv:cs.CG/0701096v2.
Together with the proof contained in arXiv:cs.CG/0701096v2, this paper
definitely proves that the general problem of tiling the hyperbolic plane with
{\it \`a la} Wang tiles is undecidable.Comment: 20 page
Constructing a uniform plane-filling path in the ternary heptagrid of the hyperbolic plane
In this paper, we distinguish two levels for the plane-filling property. We
consider a simple and a strong one. In this paper, we give the construction
which proves that the simple plane-filling property also holds for the
hyperbolic plane. The plane-filling property was established for the Euclidean
plane by J. Kari, in 1994, in the strong version
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