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.
Left-drag to zoom, right-drag to pan. Double-click to reset.
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]
Controls
| Left-drag | Draw an aspect-ratio-locked zoom selection |
|---|---|
| Right-drag | Pan the view |
| Double-click | Reset to default view |
| Zoom Out | Expand view by 2× around centre |
| Fix Aspect Ratio | Match x / Im axis range to canvas proportions |
| Fullscreen | Toggle fullscreen layout |
| Sliders | Manually set r, x, and Im axis bounds |
Both diagrams share the r axis, linked via
c = r/2 − r²/4.
Panning or zooming either canvas updates both.