We study the discretised segments generated by the iterated Tribonacci substitution and the projections of the integer points on them to some plane. After suitable transformations we get a sequence of finite two-dimensional words which tends to a doubly rotational word on Z. (Without scaling we would get the Rauzy fractal.) As an introduction we start with the corresponding case of the Fibonacc...

The Fibonacci numbers are terms of the sequence defined in a quite simple recursive fashion. However, despite its simplicity, they have some curious properties which are worth attention. In this set of notes, we will look at some of the important features of these numbers. In the first half of the notes, our attention shall be paid to the relationship of the Fibonacci numbers and the Euclidean ...

The Fibonacci cube Γn is obtained from the n-cube Qn by removing all the vertices that contain two consecutive 1s. If, in addition, the vertices that start and end with 1 are removed, the Lucas cube Λn is obtained. The number of vertex and edge orbits, the sets of the sizes of the orbits, and the number of orbits of each size, are determined for the Fibonacci cubes and the Lucas cubes under the...