The logistic map

2 figures

The map $x_{n+1} = r\,x_n(1-x_n)$ on $[0,1]$. This page exists to show what a record looks like: a figure carries the code that drew it and the numbers behind it, so the catalogue is readable by a person and by a program.

Sec. 1. Orbits (1)

Four orbits from $x_0 = 0.2$, through the period doubling into chaos.

orbits_fig1 ⤓ download
Fig. 1. Fixed point, 2-cycle, 4-cycle, chaos

Sec. 2. Bifurcation (1)

The attractor as $r$ sweeps $[2.5, 4]$; the accumulation point is near $r \approx 3.5699$.

bifurcation_fig1 ⤓ download
Fig. 2. 600 values of r, 80 iterates each after 300 discarded (a raster: 48_000 points)
rbehaviour
2.9fixed point
3.32-cycle
3.554-cycle
3.9chaotic
Where each orbit above sits