Feigenbaum (1978) discovered that the ratio of successive period-doubling bifurcation intervals converges to δ ≈ 4.6692 for any unimodal map — logistic, sine, quadratic, or otherwise. This universality arises from renormalization group theory: near each bifurcation, the dynamics converge to a universal fixed-point function under the doubling operator. The constant α ≈ 2.5029 governs the self-similar scaling of the attractor's width. These constants appear in real physical systems: Rayleigh-Bénard convection, electronic circuits, and chemical oscillators all exhibit period-doubling cascades with ratio δ before becoming chaotic.