Discrete Dynamics Gallery [work in progress...]
Here we post some pictures of the bifurcation diagrams of the Logistic map
lμ(x) = μx(1-x)
in the real line. In the graphs where the basins of attraction are included, the color
is a function of the time to get "close enough" to the attractor: red color means fast
convergence time, green color means slow convergence time.
-
Wide range:
-
Chain-Recurrent set in the range [2.9,4]x[0,1] at 3000x3000 (scaled 25%)
-
Devil-pitchfork Chain-Recurrent set in the range [3.1,4]x[0,1] at 3000x3000
-
Attractors in the range [2.5,4]x[0,1] at 5000x5000
-
Attractors & basin of attraction in the range [2.5,4]x[0,1] at 5000x5000
-
Attractors in the range [2,4]x[0,1] at 1000x750
-
Attractors & basin of attraction in the range [2,4]x[0,1] at 1000x750
-
Immediately before the Feigenbaum point:
-
Immediately after the Feigenbaum point:
-
The period-3 window:
-
Wide Range
-
Chain-Recurrent set in the range [3.8,3.9]x[0,1] at 3000x3000 (scaled 25%)
-
Devil-pitchfork Chain-Recurrent set in the range [3.1,4]x[0,1] at 3000x3000
-
Attractors in the range [3.77,3.87]x[0,1] at 1000x1000
-
Attractors & basin of attraction in the range [3.77,3.87]x[0,1] at 1000x1000
-
Attractors in the range [3.828,3.856]x[0,1] at 2000x2000
-
Attractors & basin of attraction in the range [3.828,3.856]x[0,1] at 2000x2000
-
Attractors in the range [3.828,3.856]x[0,1] at 3000x3000
-
Attractors & basin of attraction in the range [3.828,3.856]x[0,1] at 3000x3000
-
The central sub-window:
-
Chain-Recurrent set in the range [3.828,3.858]x[0.42,0.57] at 3000x3000 (scaled 25%)
-
Attractors in the range [3.831,3.856]x[0.44,0.55] at 3000x3000
-
Attractors & basin of attraction in the range [3.831,3.856]x[0.44,0.55] at 3000x3000
-
Attractors in the range [3.828,3.858]x[0.42,0.57] at 3000x3000
-
Attractors & basin of attraction in the range [3.828,3.858]x[0.42,0.57] at 3000x3000
-
Attractors in the range [3.828,3.858]x[0.42,0.57] at 5000x5000
-
Attractors & basin of attraction in the range [3.828,3.858]x[0.42,0.57] at 5000x5000