Chaos: The Bifurcation Diagram
The Bifurcation Diagram is essentially a summary of multiple Logistic Maps. For background on the Bifurcation Diagram, Google "chaos bifurcation diagram".
Here we show how to plot the bifurcation diagram of the logistic map for a parabola or sine wave.
For the parabola, we use values 2.5 < k < 4; the parabola map goes to -∞ at k=4.
For the sine, we use values 0.5 < k < 3*Π. The missing negative plot data for k < 3.1415... is a mystery.
The accuracy is very dependent on the number of k values used, given by the Δk below. Using Δk = 0.01 is a good start. Using Δk = 0.001 gives a very fine map, but takes a good 10 seconds to compute, so be patient!