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}]},
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}]},
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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