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plot question

• To: mathgroup at smc.vnet.net
• Subject: [mg71453] plot question
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Sun, 19 Nov 2006 01:10:08 -0500 (EST)

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.

• Follow-Ups:
  • Re: plot question
    • From: Christopher Arthur <caa0012@unt.edu>