File:Logistic Map Animation.gif

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Original file (1,000 × 662 pixels, file size: 913 KB, MIME type: image/gif, looped, 51 frames, 10 s)

Captions

Captions

Dynamics of logistic map for 50,000 random starting points.

Summary

[edit]
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

[edit]

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

[edit]
I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
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.

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Date/TimeThumbnailDimensionsUserComment
current19:15, 11 August 2020Thumbnail for version as of 19:15, 11 August 20201,000 × 662 (913 KB)Student298 (talk | contribs)Uploaded own work with UploadWizard

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