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Logistic_map.gif (576 × 393 pixels, file size: 1.82 MB, MIME type: image/gif, looped, 101 frames, 10 s)

Summary

Description
English: For a logistic map, depending on your choice of the parameter r, different initial conditions will: collapse to 0, collapse on a well defined curve, show a bifurcation, get in a periodic orbit, get into an aperiodic orbit.
Date
Source https://twitter.com/j_bertolotti/status/1235854410493747201
Author Jacopo Bertolotti
Permission
(Reusing this file)
https://twitter.com/j_bertolotti/status/1030470604418428929

Mathematica 12.0 code

logistic[r_, x_] := r x (1 - x)
rlist = Table[r, {r, 0, 4, 0.02}];
evo = Table[NestList[logistic[r, #] &, x0, 100], {x0, 0, 1, 0.005}, {r, rlist}];
p0 =
  Table[
   Show[
    Plot[0, {x, 0, 4}, PlotRange -> {{0, 4}, {0, 1}}, AxesLabel -> {"r", "x"}, LabelStyle -> {Bold, Black}, PlotLabel -> StringForm["Logistic map: \!\(\*SubscriptBox[\(x\), \(n + 1\)]\)=r \\!\(\*SubscriptBox[\(x\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \(n\)]\\)). n=``", t - 1]],Graphics[{PointSize[0.005], Opacity[0.3],
      Table[Point[{rlist[[r]], evo[[x0, r, t]]}], {x0, 1, Dimensions[evo][[1]]}, {r, 1, Dimensions[evo][[2]]}]}], ImageSize -> Large]
   , {t, 1, Dimensions[evo][[3]]}] ;
ListAnimate[p0]

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

Captions

logistic map dynamics for many different starting conditions

Items portrayed in this file

depicts

6 March 2020

image/gif

1,906,955 byte

10.1 second

393 pixel

576 pixel

ab72f91cbb2e3307c3277b4492fbac492b6b1bef

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current18:52, 11 August 2020Thumbnail for version as of 18:52, 11 August 2020576 × 393 (1.82 MB)Student298Reverted to version as of 09:20, 9 March 2020 (UTC)
18:51, 11 August 2020Thumbnail for version as of 18:51, 11 August 20201,000 × 654 (863 KB)Student298Higher resolution version of the animation, slightly different but essentially the same.
09:20, 9 March 2020Thumbnail for version as of 09:20, 9 March 2020576 × 393 (1.82 MB)BertoUploaded own work with UploadWizard

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