Re: plot question

• To: mathgroup at smc.vnet.net
• Subject: [mg71470] Re: [mg71453] plot question
• From: Christopher Arthur <caa0012 at unt.edu>
• Date: Mon, 20 Nov 2006 02:43:52 -0500 (EST)
• References: <200611190610.BAA23562@smc.vnet.net>

```If you're wanting opinions, mine is that just glancing at it gives me a
headache.  If you want the reader to concentrate on the math, then take
the math out of the Show[].  After glancing twice, I see that you're
essentially plotting 10 curves that differ by levels of recursion with
sine or cosine.  Perhaps it would be more clear if you made a second
function F or G in each case, and took the Plot[] out of the mess also,
so I know that you're intention is to plot these functions.  Consider
using Epilog/Prolog or SetOptions to take some of the  other stuff out
of the Plot[], so you don't even need a Show[].  k=10;
f[x_, n_] := Nest[Sin, N[x], n]
F[x_]=Array[f[x,#1],{k}];
Plot[Evaluate[F[x]],{x,0,2*Pi}]

Quoting dimitris <dimmechan at yahoo.com>:

> 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.
>
>

```

• References:
• Prev by Date: returning variable number of arguments from a Module[ ]
• Next by Date: Re: Why does this lead to an answer with complex numbers?
• Previous by thread: plot question
• Next by thread: Re: plot question