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