Re: WRI Curve and Filling Colors

• To: mathgroup at smc.vnet.net
• Subject: [mg126838] Re: WRI Curve and Filling Colors
• From: Curtis Osterhoudt <cfo at lanl.gov>
• Date: Tue, 12 Jun 2012 02:58:36 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <000001cd474a\$9997d930\$ccc78b90\$@comcast.net> <201206110402.AAA17235@smc.vnet.net>

```http://forums.wolfram.com/mathgroup/archive/2008/May/msg00634.html

It's a clever use of "maximally irrational numbers", though the ability of the human eye to differentiate hues based on that number system may preclude very practical arguments for it.

On Sunday, June 10, 2012 22:02:48 Bob Hanlon wrote:
> 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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