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MathGroup Archive 2007

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Re: Plot a simple function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74928] Re: Plot a simple function
  • From: Roger Bagula <rlbagula at sbcglobal.net>
  • Date: Wed, 11 Apr 2007 02:03:18 -0400 (EDT)
  • References: <evab3s$d6b$1@smc.vnet.net>

The Entropy map type functions made me realize that there was a sequence 
of these
mapping functions and their Integrals formed an alternation of integers  
and irrationals sequence.
{2., 2.77259, 3., 3.14159, 4., 4.66667, 5., 5.1774, 6.}
After the tent map ( K=0)  the curvatures are negative.
I don't know if this is an actually quantum sequence or not!

Clear[e, f]
(* pulse : c[1] = 2*)
f[x_, 1] := 1
(* entropy of information*)
f[x_, 2] := -x*Log[2, x] - (1 - x)*Log[2, 1 - x] /; 0 <= x <= 1;
(* Logistic map*)
f[x_, 3] := 4*x*(1 - x)
(* Sine map*)
f[x_, 4] := Sin[Pi*x]
(* Tent Map*)
f[x_, 5] := 2*x /; 0 <= x <= 1/2
f[x_, 5] := (2 - 2*x) /; 1/2 < x <= 1
(* Square root tent map : equivalent to logistic*)
e[x_] := Sqrt[2*x] /; 0 <= x <= 1/2
e[x_] := Sqrt[(2 - 2*x)] /; 1/2 < x <= 1
(* 4/3 power tent map*)
ha := 4/3
f[x_, 6] := (2*x)^ha /; 0 <= x <= 1/2
f[x_, 6] := (2 - 2*x)^ha /; 1/2 < x <= 1
(* 3/2 power tent map*)
h0 := 3/2
f[x_, 7] := (2*x)^h0 /; 0 <= x <= 1/2
f[x_, 7] := (2 - 2*x)^h0 /; 1/2 < x <= 1
(* Farey map*)
f[x_, 8] := (x/(1 - x)) /; 0 <= x <= 1/2
f[x_, 8] := ((1 - x)/x) /; 1/2 < x <= 1
(*square tent map*)
h := 2;
f[x_, 9] := (2*x)^h /; 0 <= x <= 1/2
f[x_, 9] := (2 - 2*x)^h /; 1/2 < x <= 1
c = Table[1/Integrate[f[x, n], {x, 0, 1/2}], {n, 1, 9}];
N[c]
ListPlot[c,
 PlotJoined -> True]
b =
   Table[Plot[f[x, n], {x, 0, 1}, PlotRange -> {{0, 1}, {0, 1}}], {n, 1, 9}]
Show[b]


Respectfully, Roger L. Bagula
 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 
:http://www.geocities.com/rlbagulatftn/Index.html
alternative email: rlbagula at sbcglobal.net


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