Cobweb Diagram & Iteration Sequence
Top: Cobweb diagram showing the relationship between successive iterations. The red and blue spirals start from different initial conditions (0.05 and 0.90) and converge to the attractor.
Bottom: Time series of values over 100 iterations, showing convergence behavior.
Bottom: Time series of values over 100 iterations, showing convergence behavior.
Feigenbaum Bifurcation Diagram
r = 2.80
Left diagram: Shows the full bifurcation structure from r = 0 to r = 4. The red vertical line indicates the current parameter value. The black dots represent attractor points after transient behavior has settled.