Extensions of the shannon entropy and the chaos game algorithm to hyperbolic numbers plane

In this paper, we provide extensions to hyperbolic numbers plane of the classical Chaos game algorithm and the Shannon entropy. Both notions connected with that of probability with values in hyperbolic number, introduced by Alpay et al. [Kolmogorov's axioms for probabilities with values in hyperbolic numbers, Adv. Appl. Clifford Algebras 27(2) (2017) 913-929]. Within this context, particular attention has been paid to the interpretation of the hyperbolic valued probabilities and the hyperbolic extension of entropy as well.