File:Logistic Map Animation.gif
Summary
| Description |
English: Dynamics of logistic map for 50,000 random starting points. Inspired by File:Logistic Map.gif, this is a higher resolution version which is essentially the same. |
| Date | |
| Source | Own work |
| Author | Student298 |
Mathematica 12.0 code
Note that the formula in the PlotLabel string should appear as xn+1 = r xn (1-xn) in the Mathematica notebook.
Data = {};
Many = 50000;
Data1 = {};
For[r = 1, r < Many, r++,
AppendTo[Data1, {4 r/Many, RandomReal[]}]];
AppendTo[Data, Data1]
For[n = 2, n < 52, n++,
NextData = {};
For[r = 1, r < Many, r++,
AppendTo[
NextData, {4 r/
Many, (4 r/Many)*(Data[[n - 1]][[r]][[2]])*(1 -
Data[[n - 1]][[r]][[2]])}]
];
AppendTo[Data, NextData]
]
Images = Table[
ListPlot[Data[[n]], ImageSize -> 1000, PlotRangePadding -> None,
PlotRange -> {0, 1},
PlotStyle -> {PointSize[0.0001], RGBColor["#888888"]},
AxesLabel -> {"r", "x"}, LabelStyle -> {Black, Larger},
PlotLabel ->
Style[StringTemplate[
"Logistic map: x_n+1 = r x_n (1-x_n). n = `1`"][n - 1], {Larger, Bold}]], {n, 1, 51}]
Export["logistic2.gif", Images, "DisplayDurations" -> 0.2,
AnimationRepetitions -> Infinity]
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
