several plots in manipulate

• To: mathgroup at smc.vnet.net
• Subject: [mg90754] several plots in manipulate
• From: "Cristina Ballantine" <cballant at holycross.edu>
• Date: Wed, 23 Jul 2008 05:56:46 -0400 (EDT)

```Hi,

I would like to manipulate a plot created from three different parametric
plots. I display the plot with Show[plot1,plot2,plot3] (see code below).
If I try this in Manipulate, the plots are displayed next to each other. I
need them in a single plot. I cannot combine them in a single ParameterPlot
because the options are different.

Any help is very much appreciated.

Cristina

---------------------------------------------------------------------------=
--------------

In the plot r2=2/3. In Manipulate r2 should be between r1 and 1.

r1 := 1/4
r2 := 2/3
u := Pi/3

plot1 := ParametricPlot[{{Re[
1*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[1*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
1*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[1*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
I*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[I*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
I*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[I*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-1)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-1)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -

4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-1)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-1)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-I)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-I)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-I)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -

Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-I)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}}, {t, 10^(-10), 2*Pi - 10^(-10)}, {r, 0,
r1^4*r2^4 - 10^(-6)}, PlotRange -> All,
ColorFunction -> Function[{x, y, t, r}, Hue[.5, t, r]],
PlotPoints -> 25, Mesh -> False]

plot2 := ParametricPlot[{{Re[
1*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[1*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
1*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[1*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
I*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[I*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
I*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[I*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-1)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-1)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -

4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-1)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-1)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-I)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-I)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-I)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -

Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-I)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}}, {t, 10^(-10), 2*Pi - 10^(-10)}, {r,
r1^4*r2^4 - 10^(-6), r1^4*r2^4 + 10^(-2)}, PlotRange -> All,
ColorFunction -> Function[{x, y, t, r}, Hue[1, t, r]],
PlotPoints -> 45, Mesh -> False]

plot3 := ParametricPlot[{{Re[
1*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[1*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
1*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[1*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
I*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[I*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
I*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[I*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-1)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-1)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -

4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-1)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-1)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-I)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-I)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-I)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -

Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-I)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4  *r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}}, {t, 10^(-10), 2*Pi - 10^(-10)}, {r,
r1^4*r2^4 + 10^(-2), 1}, PlotRange -> All,
ColorFunction -> Function[{x, y, t, r}, Hue[.1, t, r]],
PlotPoints -> 25, Mesh -> False]

```

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