The deterministic proliferation of the orientation of hexagonally packed cylinders (HEX) from the twinned body-centered cubic (BCC) phase is investigated by synchrotron small-angle X-ray scattering (SAXS) and rheo-optical methods for di- and triblock copolymers of styrene and isoprene (SI and SIS). Repeated heating and cooling cycles starting from an initially aligned HEX produce a proliferation of cylinder orientations from successively twinned BCC states. The evolution of the orientation distribution of HEX cylinders produces a decrease in the birefringence and increase in the modulus with each successive generation. The cylinder axes of the degenerate HEX states coincide with the <111> directions of the twinned BCC due to the epitaxial growth of cylinders from the twinned BCC. The distribution of the cylinder axes of the degenerate HEX states among the <111> directions of the twinned BCC is found to be affected by memory of the prior HEX state, which decays with annealing time in the BCC state.