@acer Incidentally, I came up with almost the exact approach as you last night, and also I think you are right that, that is what Herclau had intended.  But I didn't divide the RandomArray by 10 (never thought really if that would change the distribution relatively or not) but instead slightly changed the size of the circle to make the distribution more apparent.

t :=  (same as before)
x := Vector(N, i-> 5*sin(10*t[i])+5*I*cos(10*t[i]) + RandomArray(distribution = normal) + I * RandomArray(distribution = normal) ):
plots:-complexplot(convert(x,list),style=point,symbol=point);

Also I didn't include the datatype=complex[8] because it appeared to work the same without it.

Without adding noise on the imaginary component, I see that the noise is only generated in the x direction as pagan had earlier asked what type of distribution I wanted since I was very unclear about it.

@Erik : with regards to your minor quible - I might draw your attention to ?ArrayTools[RandomArray] the help explicitly states for distribution=normal The RandomArray(distribution = normal) function randomly generates a scalar value drawn from a normal distribution on the unit interval.  So being impossible as you say then the help file needs to be changed unless, of course, I interperetted it wrong.

@Acer : I am taking Eriks suggestion, he offers excellent advice, as do you.  But I also wanted to go a bit further. 

I appreciate all of your inputs.

@Erik : with regards to your minor quible - I might draw your attention to ?ArrayTools[RandomArray] the help explicitly states for distribution=normal The RandomArray(distribution = normal) function randomly generates a scalar value drawn from a normal distribution on the unit interval.  So being impossible as you say then the help file needs to be changed unless, of course, I interperetted it wrong.

@Acer : I am taking Eriks suggestion, he offers excellent advice, as do you.  But I also wanted to go a bit further. 

I appreciate all of your inputs.

I should have said curve instead of line and I was unsure of the type of separation I wanted.  Most likely radially I would think.

In Maple 12.02, it appears the threshold for exporting is symbolsize=6.  4 and 5 don't appear to change size and 3 produces a blank plot in the worksheet.

In Maple 12.02, it appears the threshold for exporting is symbolsize=6.  4 and 5 don't appear to change size and 3 produces a blank plot in the worksheet.

@pagan I wasn't sure how to include the imaginary component without errors.  How would you add the imaginary component in the plot.  If it is obvious, I do not see it, please show.

And I do see the signal is swamped by the noise, hence another question related to how to change the default distribution values in specific syntaxes which has not been completely addressed yet. 

@pagan I wasn't sure how to include the imaginary component without errors.  How would you add the imaginary component in the plot.  If it is obvious, I do not see it, please show.

And I do see the signal is swamped by the noise, hence another question related to how to change the default distribution values in specific syntaxes which has not been completely addressed yet. 

Yes, thanks that helps, but more generally, keeping with the distribution=uniform syntax in the ArrayTools[RandomArray] call, how would one go about changing the way the call to distribution=uniform outside the unit interval?

Using showstat(ArrayTools[RandomArray]) on lines 15,18 and 28 I suppose I could alter the numbers for normal there, can't I?  and also maybe line 10 is all I need to change for uniform, I think. Can they be changed?  Of course not recommending the change to main command programming (if it's possible?), is there a way to bypass the call instead?  I believe something similar was done with another command, but I can't recall, which leads me to my last question.

Even more general still, for any command can we substitute some options calls with our own modified version (not to replace but just to override)? 

Yes, thanks that helps, but more generally, keeping with the distribution=uniform syntax in the ArrayTools[RandomArray] call, how would one go about changing the way the call to distribution=uniform outside the unit interval?

Using showstat(ArrayTools[RandomArray]) on lines 15,18 and 28 I suppose I could alter the numbers for normal there, can't I?  and also maybe line 10 is all I need to change for uniform, I think. Can they be changed?  Of course not recommending the change to main command programming (if it's possible?), is there a way to bypass the call instead?  I believe something similar was done with another command, but I can't recall, which leads me to my last question.

Even more general still, for any command can we substitute some options calls with our own modified version (not to replace but just to override)? 

Okay now, I got it.

x:=map(Re,x):

ScatterPlot(t,x,symbol=point)

Okay now, I got it.

x:=map(Re,x):

ScatterPlot(t,x,symbol=point)

I'm unable to complete your code to get it to plot right.  In your first example, the best I can do for any output is something like this:

complexplot(convert(x, list), style = point)   

I'm missing t in the plot and can't figure it out. 

I'm unable to complete your code to get it to plot right.  In your first example, the best I can do for any output is something like this:

complexplot(convert(x, list), style = point)   

I'm missing t in the plot and can't figure it out. 

@pagan I have a bad habit of initially building code with lists in loops. 

I probably should have done it more like this

a := table():
i := 1:
while i < 100 do
   ba := (rand(-15 .. 15))():
   bb := (rand(-15 .. 15))():
   b := evalf(sqrt(ba^2+bb^2)):
   if b <= 15 and b >= 10 then a[i] := [ba, bb]:  i := i+1:  end if:
end do:
plots:-pointplot(convert(a,list));