ABSTRACT
A lot of problems deal with tilings. Some of them are construction of the computation of a given function. A rather popular construction is that of the set of prime numbers. This chapter describes a pure tiling signal in the squared grid of the Euclidean plane for computing the iterated exponential also called star-exponential. It shows that such a signal can be adapted to tilings of the hyperbolic plane, after reviewing the basics required for hyperbolic geometry. The chapter examines the reader the information needed about the hyperbolic plane, it shows how to implement the tiling of the hyperbolic plane. It explores the tiling computing a double exponential function. The chapter discusses the same for the star-exponential function. Tilings are a generic source of problems dealt with by mathematics and theoretical computer science. The mathematical approach looks at properties of tilings in connection with other branches of mathematics.
