In this project i investigate the transition from order to chaos by numerically simulating the period-doubling cascade of the Logistic Map. Through iterative computation, I identify the precise bifurcation points ($r_n$) where the system’s stabili…
In this project i investigate the transition from order to chaos by numerically simulating the period-doubling cascade of the Logistic Map. Through iterative computation, I identify the precise bifurcation points ($r_n$) where the system’s stability splits into higher-order orbits. By calculating the ratio between these successive intervals, I demonstrate the convergence toward the universal Feigenbaum constant ($\delta \approx 4.669). The study highlights how a simple, deterministic equation can lead to universal mathematical constants that govern complex chaotic behavior in nature.
I might use Google Gemini sometimes for bug fix and grammar fix, but not more than 10% of my project