Re: WRI Curve and Filling Colors

• To: mathgroup at smc.vnet.net
• Subject: [mg126833] Re: WRI Curve and Filling Colors
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Mon, 11 Jun 2012 00:02:48 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <000001cd474a\$9997d930\$ccc78b90\$@comcast.net>

```Don't know what this means, but the slope can be related to the GoldenRatio

r = RootApproximant[0.2360679774997899]

-2 + Sqrt[5]

GoldenRatio // FunctionExpand

(1/2)*(1 + Sqrt[5])

r == 2 GoldenRatio - 3

True

Bob Hanlon

On Sun, Jun 10, 2012 at 4:49 PM, djmpark <djmpark at comcast.net> wrote:
> Many thanks Bob.
>
> Picking up from what you did, I believe the colors can be specified slightly
> more simply as:
>
> curveColor[n_Integer] :=
>  Hue[Mod[0.67 + 0.2360679774997899`*(n - 1), 1], 0.6, 0.6]
> Table[curveColor[n], {n, 1, 15}] // Column
>
> The automatic FillingStyle appears to be specified by a Directive as
> follows:
>
> fillColor[n_Integer] := Opacity[0.2, curveColor[n]]
> Table[fillColor[n], {n, 1, 5}] // Column
>
> Then the question is: Does 0.2360679774997899 come from something
> interesting or is it just a trial and error choice?  And although the colors
> do not exactly repeat, they are not all that distinguishable beyond the
> first four.
>
>
> David Park
> djmpark at comcast.net
> http://home.comcast.net/~djmpark/index.html
>
>
>
> From: Bob Hanlon [mailto:hanlonr357 at gmail.com]
>
> You can readily determine the default color scheme.
>
> p = Plot[Evaluate[
>   Table[a*x, {a, 15}]],
>  {x, 0, 1}]
>
> The colors are
>
> colors = Cases[p, Hue[__], Infinity]
>
> {Hue[0.67, 0.6, 0.6], Hue[0.906068, 0.6, 0.6], Hue[0.142136, 0.6, 0.6],
> Hue[0.378204, 0.6, 0.6], Hue[0.614272, 0.6, 0.6], Hue[0.85034, 0.6, 0.6],
> Hue[0.0864079, 0.6, 0.6], Hue[0.322476, 0.6, 0.6], Hue[0.558544, 0.6, 0.6],
> Hue[0.794612, 0.6, 0.6], Hue[0.0306798, 0.6, 0.6], Hue[0.266748, 0.6, 0.6],
> Hue[0.502816, 0.6, 0.6], Hue[0.738884, 0.6, 0.6], Hue[0.974952, 0.6, 0.6]}
>
> Note that the green and blue components are constant at 0.6 and only the red
> component varies. Plotting the red component:
>
> n = 1; ListPlot[
>  c = Cases[colors,
>   Hue[r_, 0.6, 0.6] :> {n++, r},
>   Infinity]]
>
> These are lines of constant slope
>
> f[{lb_, ub_}] := FindFit[
>  Select[c, lb <= #[[1]] <= ub &],
>  a*x + b, {a, b}, x]
>
> f /@ {{1, 2}, {3, 6}, {7, 10}, {11, 15}}
>
> {{a -> 0.236068, b -> 0.433932}, {a -> 0.236068,
>  b -> -0.566068}, {a -> 0.236068, b -> -1.56607}, {a -> 0.236068,
>  b -> -2.56607}}
>
> red[n_?NumericQ] := Module[
>   {y = 0.236068 n + 0.433932},
>   y - Floor[y]];
>
> Plot[red[x], {x, 0, 15.2},
>  Epilog -> {Red, AbsolutePointSize[3],
>   Point[c]}]
>
> The colors are then
>
> color[n_Integer] := Hue[red[n], 0.6, 0.6]
>
>
> Bob Hanlon
>

--
Bob Hanlon

```

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