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Sometimes I need to plot functions that take quite a while to calculate--and sometimes I need to replot in light of what I see on the plot. Is it possible to add points to a plot one by one, as they are calculated, so that I can preview how its coming out?

In the code below, I calculate a function at 240 values of x. If I replot after every point, I'll end up with a series of 240 plots, which is not what I want. Is it possible to just draw one plot and add the newly-calculated points to it?

z[n_, x_] := Nest[#^2 + x &, x, n];
center = -1.40115518909205`60;
side = N[(3*10^-15), 60];
steps = 120;
stepSize = side/steps;
a = Table[z[-1 + 2^28, center + n*stepSize], {n, -steps, steps}];
ListPlot[a, PlotStyle -> PointSize[Small], DataRange -> {-side, side}]

(If anyone has some tips on speeding this calculation up, that would also be appreciated.)

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If you wanted to only ever have one plot the two ways come to mind. One is similar to @bbgodfrey's method but incorporating some front end code to delete the previous plot. The other is to make the plot dynamic:

a = Table[n, {n, -20, 20}];
Dynamic[ListPlot[a, DataRange -> {-1, 1}], TrackedSymbols :> {a}]

Now every time you change a the plot will change. The example below is quick and dirty. I've used Flatten to modify a but there are many other ways: Join, Append, Prepend and so on.

enter image description here

enter image description here

Edit

there are a few ways to do it without using dynamic. Here is a reference to something @Kuba posted:

SetOptions[EvaluationCell[], CellTags -> "target"]

then

NotebookWrite[Cells[CellTags -> "target"][[1]], 
 Cell[BoxData[ToBoxes@ListPlot[a, DataRange -> {-1, 1}]], "Input", 
  CellTags -> "target"]]

enter image description here

share|improve this answer
    
Thank you! Dynamic is totally new to me, so I'll have to check this out. What's that other method you mentioned? How would one delete a plot and draw a new one where it was? – Jerry Guern Feb 25 at 3:40
    
The other method would be to use SelectionMove to go back and select the previous plot and delete it. The above is cleaner – Mike Honeychurch Feb 25 at 3:55
    
Is one of these methods any better/cleaner than using Dynamic? – Jerry Guern Feb 25 at 6:06
    
Dynamic had the potential to add a point without updating the entire graphic so there could possibly be faster for large data. in the current answer both methods render a new plot each change – Mike Honeychurch Feb 25 at 10:40

I take it that you wish to add points to an existing plot without using Show. Consider the toy problem,

a = Table[n, {n, -20, 20}];
plt = ListPlot[a, DataRange -> {-1, 1}]

enter image description here

To add

newpoint = {1, 10}

do the following.

pts = Join[Catenate@Cases[plt, Point[z_] -> z, Infinity], {newpoint}];
plt /. Point[_] -> Point[pts]

enter image description here

which contains the new point, as desired. Additional points can be added by Joining or Appending them to pts.

Addendum

To have only one Plot displayed in the notebook, use

a = Table[n, {n, -20, 20}];
plt = ListPlot[a, DataRange -> {-1, 1}];
Dynamic[plt]

which displays the first plot above. Then

newpoint = {1, 10};
plt = plt /. Point[z_] :> Point[Append[z, newpoint]];

will cause the first plot to be replaced by the second.

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No, that's not adding the point to the already-drawn plot, that's redrawing the plot with a new point. If I do this after each of 240 new points, I'll have a series of 240 plots scrolling past. – Jerry Guern Feb 25 at 3:14

From the OP: This is just a demo of the Dynamic[] method Mike recommended above. This is exactly the effect I wanted to create for when I'm looking at a bifurcation point of a slooow calculation.

(* Function and endpoints *)
z[n_, c_] := Nest[#^2 + c &, c, n];
center = -1.40115518909205`60;
delta = N[(1*10^-12), 60];
r=22;
f[x_] := z[-1 + 2^r, center + x];


(*This array t makes the data pts fill in from the centre out, in layers*)
t = Flatten[{-1, 1, 0, Table[Table[{-i, i}, {i, 1, -1 + 2^j, 2}]/(2^j), {j, 1, 6}]}];

(* Initialize the plot with the first, middle, last points *)
fml = delta*{-1, 0, 1} ; a = Transpose[{fml, f[fml]}];
Dynamic[ListPlot[a, DataRange -> {-delta, delta}], TrackedSymbols :> {a}]
Do[
    x = t[[i]]*delta;
    AppendTo[a, {x, f[x]}], {i, 1, Length[t]}]

Give it a few seconds, because it's slow (which was the point of all this), and depending on how you change the parameters the initial plot might not plot because of values of f[x] with no sig figs. If it's too slow on your computer, decrease r a bit. Sorry, I don't know how to create/upload a cool animation like Mike did.

fadeIn

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