Single trajectory — xn vs. n at r = 3.900–
This is a 2D companion to the site's 3D bifurcation diagram. Instead of a rendered-once texture, every column of this diagram is computed live from the exact logistic recurrence x(n+1) = r·x(n)·(1−x(n)): the current r/x window is iterated per pixel column on every render, so left-drag panning, shift-drag rectangle zoom and mouse-wheel zoom all trigger a genuine recomputation at the new scale rather than a crop of a cached image — which is how the diagram's true self-similarity keeps revealing new period-doubling copies as you go deeper. A second panel below plots a single orbit, xn against the iteration number n, for any r you choose with the slider or by clicking directly on the diagram, so the fixed points, periodic cycles and chaotic wandering that make up the diagram above can be read one trajectory at a time.