Semigroups and the self-similar structure of the flipped tribonacci substitution Original Research Article

Using the numeration system associated to the substitution 1 → 12, 2 → 31, 3 → 1, we define a binary operation, which generates a semigroup on a subset of N. This semigroup represents the self-similar structure defined by an Iterated Function System (IFS) on the dynamical system associated to this substitution.