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MathGroup Archive 2006

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Re: plot question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71618] Re: plot question
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Sat, 25 Nov 2006 05:36:57 -0500 (EST)
  • References: <ejot06$n62$1@smc.vnet.net>

Certainly something like the following is by far better (David Park
thanks a lot for your invaluable comunication).

f[x_][n_] := Nest[Sin, x, n]

Show[(Plot[f[x][#1], {x, 0, 2*Pi}, DisplayFunction -> Identity] & ) /@
Range[10], DisplayFunction -> $DisplayFunction,
   Epilog -> {{Text[StyleForm["n=10", FontSize -> 15], {Pi/2, 0.35}],
Text[
       StyleForm[HoldForm[sin(sin(sin(... sin(x)))) , n times],
FontWeight \[Rule] Bold, FontSize \[Rule] 16]
       , {(3*Pi)/2 - 0.1, 1/2 + 0.3}]}, {Text[StyleForm["n=1", FontSize
-> 15], {Pi/2, 1.15}]}}, ImageSize -> 700,
   Frame -> {True, True, False, False}, Axes -> {True, False},
AxesStyle -> {AbsoluteDashing[{2, 4}]}, FrameLabel -> (
      StyleForm[#1, FontSize \[Rule] 16]
       & ) /@ {x, HoldForm[f[x, n]]}, TextStyle -> {FontSize -> 14,
FontFamily -> "Times"},
   PlotLabel -> StyleForm["Sine Iteration\n", FontSize -> 18,
FontWeight -> "Bold"],
   FrameTicks -> {Range[0, 2*Pi, Pi/2], Range[-1, 1, 1/2]}, PlotRange
-> {{-0.001, 2*Pi}, {-1.01, 1.2}}];


dimitris wrote:
> Hello to all.
>
> "Less in More"!
>
> But do the following plot contain enough details for the reader to
> understand the "mathematics" and in the same time not discard him with
> a lot of useless details (such as many legends, a lot of colors
> e.t.c.)?
>
> f[x_, n_] := Nest[Sin, N[x], n]
>
> Show[(Plot[f[x, #1], {x, 0, 2*Pi}, PlotStyle -> Hue[#1/11],
> DisplayFunction -> Identity] & ) /@ Range[10],
>    Graphics[{{Hue[1/11], Line[{{Pi + 0.5, 1 - 0.1}, {3*(Pi/2) - 0.5, 1
> - 0.1}}]},
>      {Hue[10/11], Line[{{Pi + 0.5, 1/2 - 0.1}, {3*(Pi/2) - 0.5, 1/2 -
> 0.1}}]}, {Text["n=10", {3*(Pi/2), 1/2 - 0.1}]},
>      {Text["n=1", {3*(Pi/2), 1 - 0.1}]}}], DisplayFunction ->
> $DisplayFunction, ImageSize -> 600,
>    Frame -> {True, True, False, False}, Axes -> {True, False},
> AxesStyle -> {AbsoluteDashing[{2, 4}]},
>    FrameLabel -> TraditionalForm /@ {x,
> HoldForm[Sin[Sin[Sin["..."*Sin[x]]]]*",  n times"]},
>    TextStyle -> {FontSize -> 14, FontFamily -> "Times"}, PlotLabel ->
> "Sin Iteration\n",
>    FrameTicks -> {Range[0, 2*Pi, Pi/2], Range[-1, 1, 1/2]}, PlotRange
> -> {{-0.001, 2*Pi}, {-1.001, 1}}];
>
> g[x_, n_] := Nest[Cos, N[x], n]
>
> Show[(Plot[g[x, #1], {x, 0, 2*Pi}, PlotStyle -> Hue[#1/11],
> DisplayFunction -> Identity] & ) /@ Range[10],
>    Graphics[{{Hue[10/11], Line[{{Pi, 1 - 0.05}, {3*(Pi/2) - 1, 1 -
> 0.05}}]},
>      {Hue[1/11], Line[{{Pi, 1/2 - 0.1}, {3*(Pi/2) - 1, 1/2 - 0.1}}]},
> {Text["n=1", {3*(Pi/2) - 0.5, 1/2 - 0.1}]},
>      {Text["n=10", {3*(Pi/2) - 0.5, 1 - 0.05}]}}], DisplayFunction ->
> $DisplayFunction, ImageSize -> 600,
>    Frame -> {True, True, False, False}, Axes -> {True, False},
> AxesStyle -> {AbsoluteDashing[{2, 4}]},
>    FrameLabel -> TraditionalForm /@ {x,
> HoldForm[Cos[Cos[Cos["..."*Cos[x]]]]*",  n times"]},
>    TextStyle -> {FontSize -> 14, FontFamily -> "Times"}, PlotLabel ->
> "Cosine Iteration\n",
>    FrameTicks -> {Range[0, 2*Pi, Pi/2], Range[-1, 1, 1/2]}, PlotRange
> -> {{-0.001, 2*Pi}, {-1.001, 1}}]; 
> 
> 
> Thanks a lot.


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