WRI Curve and Filling Colors

• To: mathgroup at smc.vnet.net
• Subject: [mg126830] WRI Curve and Filling Colors
• From: "djmpark" <djmpark at comcast.net>
• Date: Mon, 11 Jun 2012 00:01:46 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```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

```

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