Plotting colorfunctions over multiple parametric curves

• To: mathgroup at smc.vnet.net
• Subject: [mg125188] Plotting colorfunctions over multiple parametric curves
• From: Andrew Green <kiwibooga at googlemail.com>
• Date: Mon, 27 Feb 2012 06:40:54 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Hi there

I am a bit stuck with this one. I have several curves (circles in this
case) I want to plot at the same time. Each circle also has its own
function defining a unique potential as a function of theta around the
curve. I want to take advantage of Mathematica's colorfunction color
scaling and show the potential around each curve in a color scaled to
the min and max values for the entire set of circle potentials. I get

n = 5; (*number of circles*)

potential[theta_, i_] := Sin[2*i*theta];

circle[i_, theta_] := {x[i] + r[i]*Cos[theta], y[i] +
r[i]*Sin[theta]}; (*x,y, and r are earlier defined vectors of

ParametricPlot[
Evaluate@Table[circle[i, theta], {i, 1, n}], {theta, 0, 2 Pi},
PlotStyle -> Thick, Axes -> False,
ColorFunction ->
Function[{x, y, theta}, ColorData["TemperatureMap"][theta]]];

I can get a nice rainbow color around each circle  but it is the same
for all because I can only seem to define one colorfunction and cannot
incorporate the potential function which varies for each circle "i".

Any help would be most appreciated.

Andrew Green

```

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