The article developed the mathematical model for the synthesis of ornamental images and implemented the software editor of ornamental images, based on symmetry theory. The paper shows the fundamental role of symmetry. It is analyzed that the symmetry theory methods are used in physics, chemistry, biology, and engineering. It was found that symmetry is based on transformation and storage. In addition, the symmetrical system is based on a set of invariants that are built according to certain rules.

Symmetry of energy

Based on the principle of symmetry, we  propose a universal expression of the energy of  physical system. If we accept a generalized coordinate as an argument, we come to potential energy; if we accept a generalized velocity as an argument, we come to kinetic co-energy. Here, like in the variational principle, the concept of kinetic energy does not work. The examples of application relate to electromagnetic fields, electro­magnetic circuits, and mechanics of concentrated masses.