About the Garden of Eden Theorems for Cellular Automata in the Hyperbolic Plane

The Garden of Eden theorems are well known theorems established by Moore and Myhill in the early sixties connecting injectivity and surjectivity for the global function of cellular automata in the (Euclidean) plane. In this paper, it is shown that the properties established by Moore and Myhill are no more true for cellular automata in the hyperbolic plane.