File:Logistic map.gif
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This is a file from the Wikimedia Commons. The description on its description page there is shown below.
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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:
 
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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.
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File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Dimensions | User | Comment | |
|---|---|---|---|---|
| current | 11:52, 11 August 2020 | 576 × 393 (1.82 MB) | Student298 | Reverted to version as of 09:20, 9 March 2020 (UTC) |
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