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In this paper we provide extensions to hyperbolic numbers plane of theclassical Chaos game algorithm and the Shannon entropy. Both notions connectedwith that of probability with values in hyperbolic number, introduced by D.Alpay et al \cite{eluna}. Within this context, particular attention has beenpaid to the interpretation of the hyperbolic valued probabilities and thehyperbolic extension of entropy as well.

Extensions of the Shannon Entropy and the Chaos Game Algorithm to Hyperbolic Numbers Plane