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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- Re: WRI Curve and Filling Colors