Bifurcation Diagram Viewer

The logistic map xn+1 = r · xn(1 − xn) models population dynamics. As r increases, the long-term population transitions from a stable fixed point into period-doubling cascades and chaos. The Mandelbrot set shares the same parameter axis via c = r/2 − r²/4. Drag to zoom. Double-click to reset.

2.5000
4.0000
0.0000
1.0000
-1.5000
1.5000
Logistic Map — Bifurcation Diagram
r: [2.5, 4.0]    x: [0.0, 1.0]
Mandelbrot Set — real axis aligned via c = r/2 − r²/4
Re(c): [−2.000000, −0.312500]    Im(c): [−1.5, 1.5]