# Replacement variable in list plot

I would like the replacement:

/. {ComplexInfinity -> 0}


to be treated as a variable.

I am trying to overlay the following list plots:

g1 = (d = (q = 20;
f = (lop =
Transpose[{Flatten[
Reverse[
Table[Zeta[y], {y, 0, q}]] /. {ComplexInfinity -> 0}],
Flatten[Table[x^n, {n, 0, q}]]}];
{#1*#2} & @@@ lop);
Flatten[f];
Total[f]);
sol = Solve[d == 0];
r = ListPlot[{{Re@x, Im@x} /. sol}, AspectRatio -> Automatic, PlotStyle -> Black];
Show[r, PlotRange -> {{-q/10, q/3}, {-q/10, q/10}}, Axes -> False, ImageSize -> 800]);

g2 = (d = (q = 20;
f = (lop =
Transpose[{Flatten[
Reverse[
Table[Zeta[y], {y, 0, q}]] /. {ComplexInfinity -> 1}],
Flatten[Table[x^n, {n, 0, q}]]}];
{#1*#2} & @@@ lop);
Flatten[f];
Total[f]);
sol = Solve[d == 0];
r = ListPlot[{{Re@x, Im@x} /. sol}, AspectRatio -> Automatic, PlotStyle -> Black];
Show[r, PlotRange -> {{-q/10, q/3}, {-q/10, q/10}}, Axes -> False, ImageSize -> 800]);

...


For:

Show[{g1, g2, g3.....}]


Is there an easier way to do this - ie, in a single command?

-

cplot[m_] := g1 = (d = (q = 20;
f = (lop =
Transpose[{Flatten[
Reverse[
Table[Zeta[y], {y, 0, q}]] /. {ComplexInfinity -> m}],
Flatten[Table[x^n, {n, 0, q}]]}];
{#1*#2} & @@@ lop);
Flatten[f];
Total[f]);
sol = Solve[d == 0];
r = ListPlot[{{Re@x, Im@x} /. sol}, AspectRatio -> Automatic,
PlotStyle -> Black];
Show[r, PlotRange -> {{-q/10, q/3}, {-q/10, q/10}}, Axes -> False, ImageSize -> 800])


Now you get the first plot with cplot[0] and the second with cplot[1]. You can plot many different ones with (for instance)

cplot[#] & /@ Range[5]


which plots the first 5.

-
@ Bill s = Many thanks for your help on this - works really well :-) – martin Nov 4 '13 at 21:01
@ Bill s, Is there any way I could use something similar to Show[cplot[Range[5]]]? – martin Nov 4 '13 at 21:02
@ Bill s, Can't seem to get it to work on similar plots...:-/ – martin Nov 4 '13 at 21:16
I've updated to show you how to make it work on many. You need only define the functions -- be careful of the syntax, note the := and the underscore m_ (two common early mistakes). – bill s Nov 4 '13 at 22:57
@ Bill s, Many thanks - realised resizing issue with other plots - update really useful :-) – martin Nov 4 '13 at 23:07