My problem is that my manipulate does not 'wait' for the graphics to be fully rendered before moving on to the next step when playing the variable n. See code and picture below:
unitcircle =
ParametricPlot[{Re[Exp[I*t]], Im[Exp[I*t]]}, {t, 0, 2*\[Pi]},
PlotStyle -> {Red}];
Options[unitcircle, PlotRange];
unitdisc =
ParametricPlot[{Re[r*Exp[I*t]], Im[r*Exp[I*t]]}, {r, 0, 1}, {t, 0,
2*\[Pi]}, PlotStyle -> {Red}, PlotRangePadding -> 0.25,
ImagePadding -> {{Automatic, Automatic}, {Automatic, 10}}];
Manipulate[a = 1/2;
f[z_] := \[Alpha]*(z + a)/(1 + Conjugate[a]*z);
\[CurlyPhi][z_, n_] := Nest[f, z, n];
b = (\[Alpha] -
1 + \[Sqrt]((\[Alpha] - 1)^2 + 4*\[Alpha]*Abs[a]^2))/(2*
Conjugate[a]);
bImage = Graphics[Locator[{Re[b], Im[b]}]];
bImagelabel = Graphics[Locator[{Re[b] + 0.1, Im[b] + 0.15}, "\!\(\*
StyleBox[\"\[Xi]\",\nFontSize->36]\)"]];
fimage[n] =
ParametricPlot[{Re[\[CurlyPhi][0.25*(1 - I) + r*Exp[I*t], n]],
Im[\[CurlyPhi][0.25*(1 - I) + r*Exp[I*t], n]]}, {r, 0, 0.5}, {t,
0, 2*\[Pi]}];
If[Orbit,
Show[unitdisc, bImage, bImagelabel, Table[fimage[m], {m, 0, n, 1}],
PlotLabel ->
If[n == 0, B,
Table[If[m == 0, B, (\[CurlyPhi]^m)[B]], {m, 0, n, 1}]] ],
Show[unitdisc, bImage, bImagelabel, fimage[n],
PlotLabel -> If[n == 0, B, (\[CurlyPhi]^n)[B]]] ], {{\[Alpha], 1,
"\!\(\*
StyleBox[\"\[Alpha]\",\nFontSize->24]\)"}, {1, (1 + I)/Sqrt[2]},
ControlType -> PopupMenu},
{{n, 0, "\!\(\*
StyleBox[\"n\",\nFontSize->24]\)"}, 0, 5, 1},
{{Orbit, True, "\!\(\*
StyleBox[\"Show\",\nFontSize->18]\)\!\(\*
StyleBox[\" \",\nFontSize->18]\)\!\(\*
StyleBox[\"Orbit\",\nFontSize->18]\)"}, {True, False}},
SaveDefinitions -> True]
Is there something wrong with my code? Indeed Mathematica never seems to finish calculating. I fear that this may be something to do with my computer as the following neat example from the documentation on Manipulate also doesn't play smoothly when I run the code locally.
Manipulate[
ContourPlot[
q1/Norm[{x, y} - p[[1]]] + q2/Norm[{x, y} - p[[2]]], {x, -2,
2}, {y, -2, 2}, Contours -> 10], {{q1, -1}, -3, 3}, {{q2, 1}, -3,
3}, {{p, {{-1, 0}, {1, 0}}}, {-1, -1}, {1, 1}, Locator},
Deployed -> True]
I think my computer is more than capable of performing the calculations (1.7GHz i7 with 8GB RAM) but i cannot explain this behaviour in Mathematica 9.0.1.0 Student Edition.
I am more than happy to learn more about Manipulate and Dynamic but I want to understand what is going wrong here first.
Any help much appreciated.
