On Recursive Hyperbolic Fibonacci Quaternions

Fibonacci Sequences of Quaternions

In this paper Fibonacci sequences of quaternions are introduced, generalizing Fibonacci sequences over commutative rings, and properties of such sequences are investigated. In particular we are concerned with two kinds of Fibonacci sequences of generalized quaternions over finite fields Fp, with p an odd prime, and their periods.

Fibonacci words, hyperbolic tilings and grossone

In this paper, we study the contribution of the theory of grossone to the study of infinite Fibonacci words, combining this tool with the help of a particular tiling of the hyperbolic plane : the tiling {7, 3}, called the heptagrid. With the help of the numeral system based on grossone, we obtain a richer family of infinite Fibonacci words compared with the traditional approach. ACM-class: F.2....

Fibonacci words in hyperbolic Pascal triangles

The hyperbolic Pascal triangle HPT 4,q (q ≥ 5) is a new mathematical construction, which is a geometrical generalization of Pascal’s arithmetical triangle. In the present study we show that a natural pattern of rows of HPT 4,5 is almost the same as the sequence consisting of every second term of the well-known Fibonacci words. Further, we give a generalization of the Fibonacci words using the h...

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Puzzle Geometry and Rigidity: the Fibonacci Cycle Is Hyperbolic

We describe a new and robust method to prove rigidity results in complex dynamics. The new ingredient is the geometry of the critical puzzle pieces: under control of geometry and “complex bounds”, two generalized polynomial-like maps which admits a topological conjugacy, quasiconformal outside the filled-in Julia set are, indeed, quasiconformally conjugated. The proof uses a new abstract remova...