Among Sturmian words, some of them are morphic, i.e. fixed point of a non-identical morphism on words. Berstel and Séébold (1993) have shown that if a characteristic Sturmian word is morphic, then it can be extended by the left with one or two letters in such a way that it remains morphic and Sturmian. Yasutomi (1997) has proved that these were the sole possible additions and that, if we cut th...

An approach to the calculation of local canonical morphic heights is described, motivated by the analogy between the classical height in Diophantine geometry and entropy in algebraic dynamics. We consider cases where the local morphic height is expressed as an integral average of the logarithmic distance to the closure of the periodic points of the underlying morphism. The results may be though...

Relatively morphic submodules are defined and a new class of modules between morphic and Hopfian modules is singled out. Special care is given to the Abelian groups case.

Given an infinite word x over an alphabet A, a letter b occurring in x, and a total order σ on A, we call the smallest word with respect to σ starting with b in the shift orbit closure of x an extremal word of x. In this paper we consider the extremal words of morphic words. If x = g(fω(a)) for some morphisms f and g, we give two simple conditions on f and g that guarantees that all extremal wo...

From the homotopy groups of two cubic spherical 3-manifolds we construct the iso-morphic groups of deck transformations acting on the 3-sphere. These groups become the cyclic group of order eight and the quaternion group respectively. By reduction of representations from the orthogonal group to the identity representation of these subgroups we provide two subgroup-periodic bases for the harmoni...

Category computation theory deals with a web-based systemic processing that underlies the morphic webs, which constitute the basis of categorial logical calculus. It is proven that, for these structures, algorithmically incompressible binary patterns can be morphically compressed, with respect to the local connec-tivities, in a binary morphic program. From the local connectivites, there emerges...

Mix-automatic sequences form a proper extension of the class of automatic sequences, and arise from a generalization of finite state automata where the input alphabet is state-dependent. In this paper we compare the class of mix-automatic sequences with the class of morphic sequences. For every polynomial φ we construct a mix-automatic sequence whose subword complexity exceeds φ. This stands in...

Let w be a morphic word over a finite alphabet Σ, and let ∆ be a nonempty subset of Σ. We study the behavior of maximal blocks consisting only of letters from ∆ in w, and prove the following: let (ik, jk) denote the starting and ending positions, respectively, of the k’th maximal ∆-block in w. Then lim supk→∞(jk/ik) is algebraic if w is morphic, and rational if w is automatic. As a result, we s...