What initial value of r should you use?

[MKLau]

Simulating population dynamics for the logistic difference equation where the "biotic potential" parameter, r, is altered.

[MKLau]

[MKLau]

The value of the chaotic boundary is exactly 3.570.

In this simulation, the number of basins (i.e., attractors of x when rounded to 4 decimals) was counted for values of r from 1 to 4 at the hundredths place starting from an initial value of x = 0.1.

In order to control for the transience period, the initial 2000 values were removed.

At r = 3.570, the number of basins immediately exceeds 100.

[MKLau]

There is another area of chaotic behavior around 3, but tuning is very fine within this region.

[MKLau]

Using a threshold of 3.57, which is what was also initially stated by May 1976.

[MKLau]

Here is a better figure that shows more useful regions with moderate numbers of attractors.

[MKLau]

Move a fixed distance across each threshold of attractor number as determined by the maximum distance possible from the 4th attractor set into chaos.