A data structure in a global description of sequences is presented. The structure consists of infinite hierarchical levels. We can view the elements as those composed of elements from the lower levels. The key interest in the structure is that it has two distinctive representations, that is, algebraic and geometric, which complement each other. In the first one the elements are integer relations suggesting that ultimate building blocks are just integers from which the structure develops as one undivided whole. In the second one the elements are two-dimensional geometric patterns which upon visualization give a picture of hierarchical formations. The picture contains nonlocal order and large symmetry. Global optimization problems formulated in terms of the structure are given to show its descriptive potentialities. Well-known geometric objects appear in a new way as solutions to the problems.