  In this paper, a new method for generation of infinite series of symmetric
identities written for exponential sums in real numbers is proposed. Such
systems have numerous applications in theory of numbers, chaos theory,
algorithmic complexity, dynamic systems, etc. Properties of generated
identities are studied. Relations of the introduced method for generation of
symmetric exponential sums to the Morse-Hedlund sequence and to the theory of
magic squares are established.
