Ordered fractal semigroups as a model of computation

We introduce the notion of an ordered (generalized) fractal semigroup and show that it characterizes ordered non-Archimedean quasi-metric semigroups. With the help of this characterization, several properties of ordered fractal structures are discussed. Our study is motivated, in great part, by the fact, proved here, that the structure of an ordered non-Archimedean quasi-metric semigroup provides an efficient setting to interpret the properties of several interesting examples of spaces which appear in some fields of theoretical computer science and image processing, respectively.