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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.
>
>
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