Talk:Logistic map

message: :The logistic map is related to the Mandelbrot set by the equation c=(1-(r-1)2)/4.
I can't follow the algebra here. Mandelbrot is z[n+1] = z[n]^2 + c and logistic is x[n+1] = r x[n] (1-x[n]). I don't think the formula given above converts these formulas into each other. AxelBoldt 02:24 Sep 30, 2002 (UTC)
: I agree.
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Rewrite the logistic map as xn+1 = r ( 1/4 - (xn-1/2)2) and use the change of variables: zn = r(1/2 - xn). Result: zn+1 = zn2 + c 
with c=(1-(r-1)2)/4. 
Abelian (talk) 21:55, 12 August 2009 (UTC)
thread_title: Very old discussions

message: if r = 4, the logistic map appears to be solvable:
set
\,\! \phi = \cos^{-1}(1 - 2 x_0) 
then if
\,\! x_{n+1} = 4 x_n (1 - x_n) 
we have
 x_n = \frac{1}{2} - \frac{1}{2} \cos (2^n \phi) 
which can be easily checked.
Scythe33 20:55, 18 December 2006 (UTC)
thread_title:  note 

message: There are methods for proving that period 3 begins at exactly r = 1 + Sqrt(8).  I can provide a published proof if necessary, but also did the proof myself as a presentation in a chaos theory class.  I think this section could benefit by mentioning this.
68.55.58.255 07:41, 23 May 2007 (UTC)
thread_title:  Chaos (or period 3) begins at precisely r = 1 + Sqrt(8) 

message: It would be interesting to read about connections to biology. Are there interesting observations in nature predicted by this? (Most interesting seems the range 3-3.45)  —Preceding unsigned comment added by 130.242.107.211 (talk) 02:55, 7 April 2008 (UTC)
thread_title:  Biology 

message: There is another way, using WEBPLOT program:
 XMIN : 0
 XMAX : 1
 XSCL : .1
 YMIN : 0
 YMAX : 1
 YSCL : .1
 XINIT : $A2/.5+
 WEBSTART : 0
 WEBSTOP : 50
 CURRENT : 1'-'*$B1+2**
 REFERENCE : '
--zzo38(✉) 01:24, 23 April 2010 (UTC)
thread_title:  Logistic map with WEBPLOT 

message: The first graph on the page (the animation) has mislabeled axes. The horizontal axis should be "n" to be consistent with the equation given in the article. Took me forever to figure out what it was talking about. I'd do it myself but I don't know how to make animated gifs.
205.175.97.169 (talk) 06:56, 19 May 2014 (UTC)
thread_title:  Inconsistent diagram 

message: Should there be description on what happens if the value of r is below 0? --Artman40 (talk) 13:58, 20 October 2014 (UTC)
replies: text: The population goes negative, which doesn't really make sense as a population model? I imagine that's why nobody seems to have bothered to consider this case. Double sharp (talk) 10:09, 27 March 2015 (UTC)
replies: text: I was wrong about this: MathWorld has a page considering r = −2, which also admits an exact solution. Double sharp (talk) 12:09, 31 August 2018 (UTC)
thread_title: r values below 0

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thread_title:  External links modified 

message: These two graphs have to be some of the worst I've ever seen. They are so badly labelled, and give no idea to a reasonable user as to what the they are showing (the right graph specifically). "Parameter" should at least be labelled "parameter, r", and none of t, T, f and k are anywhere defined properly. And "[n] t=nT" is not how you properly label an axis. First, either it is "t" or it is "n" (and not "[n]" either), and secondly, some description would be nice. I've seen better graphs than this on vixra. It needs to be sorted out or removed completely, unfortunately. Krea (talk) 20:58, 8 September 2019 (UTC)
thread_title:  Badly labelled graphs