ABSTRACT: We present a spatial array of Lorenz oscillators, with each cell lattice in the chaotic regime. This system shows spatial ordering due to self-organization of chaos synchronization after a bifurcation. It is shown that an array of such oscillators transformed under a discrete symmetry group, does not maintain the global dynamics, although each transformed unit cell is locally identical to its precursor. Alternatively, it is shown that in a 1-dimensional lattice, the coupling destroy the chaotic behavior but there are similar global behaviors between both coupled arrays, suggesting that is the local equivariance which controls the dynamics.