Fibonacci tracks in quadratic fields (Q2883412)

In his paper ``The Fibonacci track form, with applications in Fibonacci vector geometry'', Notes Number Theory Discrete Math. 4, No. 4, 135--147 (1998)], the author defined the concept of a Fibonacci track as follows. Let \(S\) be a fixed set and let operation \(\oplus : S \times S \rightarrow S\) be defined over \(S\). A track in \(S\), relatively to \((a, b)\) and \(\oplus\), is the sequence of elements of \(S\) which is generated by the recurrence NEWLINE\[NEWLINEx_{n+2} = x_{n+1} \oplus x_n, \text{ with \(x_0 = a, x_1 = b,\) and }(a, b) \in S \times S.NEWLINE\]NEWLINE In the present paper, different tracks, generated by different sets \(S\) and operations \(\oplus\) are constructed and some interesting properties of them are studied.