Deterministic Chaos

The Univrsal Function

While the proof of the existence of this universal function is very subtle, there is a relatively easy way to get a picture of how complicated it looks.

First we graph a high iterate of the logistic map with a superstable 2-cycle.

Next we graph a high iterate of the logistic map with a superstable 4-cycle,

and a high iterate of the logistic map with a superstable 8-cycle.

Finally, we give a hint of the fractal nature of the universal function.

Return to Universality of the Logistic Map Bifurcation Diagram.

First we graph a high iterate of the logistic map with a superstable 2-cycle.
Next we graph a high iterate of the logistic map with a superstable 4-cycle,
and a high iterate of the logistic map with a superstable 8-cycle.
Finally, we give a hint of the fractal nature of the universal function.