Here are the graphical iteration and histogram plots for s = 3.828. Most points cluster around the x-values that will become the 3-cycle, but some points still wander between these values.

On the left below is the graphical iteration for L^{3}(x). We have not
quite reached the tangent bifurcation, so the
graph is very close to the diagonal, but has not yet crossed it.

A magnification (right) reveals a consequence of not yet crossing the diagonal.
Graphical iteration
gets stuck for a while in each of these narrow *throats*, but then escapes.

Iterates of L^{3}(x) being stuck near fixed points implies iterates of L(x) get
stuck near the 3-cycle.

Could intermittency be a source of pleasing mixtures of novelty and familiarity?

Return to Deterministic Chaos.