Where it shows up
The same forking picture appears far from ecology. You get it in a dripping tap as the flow rate rises, in the current through a driven diode circuit, in cardiac rhythms sliding toward fibrillation, and in models of turbulence onset. Because the doubling rate is universal, an engineer measuring period-doublings in a laser and a biologist counting them in an insect population read the same number off completely different apparatus. The route into chaos has a fixed accent, whatever the system speaking it.
The knobs
- r min: sets the left edge of the sweep, the lowest growth rate on screen. Slide it toward 3 to zoom into the first few forks.
- r max: sets the right edge. Push it to 4.0 to include the full chaotic band and the period windows inside it.
- Current r: moves the orange marker and drives the cobweb inset, so you can inspect exactly what one slice is doing.
- Iterations: how many steps each column runs. More iterations give a cleaner attractor and sharper forks, at the cost of a slightly longer recompute.
- Cobweb inset: toggles the top-corner staircase that traces the map bouncing between the parabola and the line for your current .