Formation of square patterns using a model alike Swift-Hohenberg

Mechanisms for pattern formation in biological organisms and chemical reactions have been broadly studied in last half of past century, because of they were frequently observed in many experiments. Traditional static patterns on the plane are patches forming hexagons, stripes and inverted hexagonal patches. Frequently, they are studied using reaction-diffusion models. The equation of Swift-Hohenberg has also been a paradigm for the formation of these structures, and for studies of localized patterns. In this paper, the behavior of a new equation similar to Swift-Hohenberg is analyzed, being able to produce square patterns having different shapes and sizes.