This project investigated whether the Feigenbaum number and Lyapunov exponent, which characterize chaos, are universal across different chaotic systems. Computational programs were developed to plot bifurcation diagrams and Lyapunov exponent plots for various maps, including the logistic, sine, and Gaussian maps. The results showed that the logistic and sine maps exhibited similar bifurcation structures and Lyapunov exponent behavior, indicating these characteristics are universal for unimodal maps. In contrast, the Gaussian map displayed distinct bifurcation and exponent patterns, only becoming briefly chaotic before returning to periodic behavior.