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.