Very sensitive responses to external forces are found near phase transitions. However, transition dynamics and preequilibrium phenomena are difficult to detect and control. We have observed that the equilibrium domain structure following a phase transition in ferroelectric and ferroelastic BaTiO_{3} is attained by halving of the domain periodicity multiple times. The process is reversible, with periodicity doubling as temperature is increased. This observation is reminiscent of the period-doubling cascades generally observed during bifurcation phenomena, and, thus, it conforms to the "spatial chaos" regime earlier proposed by Jensen and Bak [Phys. Scr. T 9, 64 (1985)PHSTER0281-184710.1088/0031-8949/1985/T9/009] for systems with competing spatial modulations.