Deterministic Chaos

Renormalization

Here we see bifurcation diagrams for L²(x),

the green points are generated by taking the initial point in the upper trapping square,

the red points are generated by taking the initial point in the upper trapping square.

The s-value where both diagrams seem to expand outward to the full bifurcation diagram is exactly the value where the graphs extend outside the trapping squares.

(But is the full diagram really full? Can you see some differences bewteen the red and green pieces? Look in the 3-cycle window.

Combing the two does give the full bifurcation diagram.

return to outside the trapping square.