Although dynamical systems of integers have been thoroughly studied, the main focus has been on metrizable dynamics. It is known that the universal minimal flow is non-metrizable and what the underlying topological space is, but how integers act on it is not at all understood. In this talk, we will discuss observations on the relationship between the universal minimal flow of the square of integers with square of the universal minimal flow of integers. This is a joint work with Aleksandra Kwiatkowska.