Clicking on any Line of Code causes Plotted Points to Vanish

Question

Bug introduced in 11.0 or earlier and persisting through 11.3.
Related but non-identical bug present in 10.0-10.4.
Reported to Worfram, Inc as CASE:3926732

---

$Version
(* "11.1.1 for Microsoft Windows (64-bit) (April 18, 2017)" *)

p1 = Plot[{Abs[5 x], -Abs[x/5]}, {x, -2, 2}, PlotRange -> {-2, 2}];
zz[{x_, y_}] := Piecewise[{{{3 /5 x -  y + 32/100 , x}, -1/5 Abs[x] <= y <= 
 5 Abs[x]}}, 
    {4/5 x + y + 52/100, x}]
p2 = ListPlot[NestList[zz, {.384, .384}, 212]]
p3 = Show[p1, p2]

Now, if I click on any line of code in the notebook, the points in the second plot vanish from the screen, leaving just the lines. I imagine that Show cannot cope with the extreme difference in PlotRange between the two plots. Nonetheless, I find this bizarre and would welcome an explanation. By the way, decreasing the third argument of NestList to 211 eliminates this behavior, while increasing that argument substantially (say, to 1000) causes both plots to exhibit this behavior.

Edit: To be more explicit, is this a bug?

Addition: In versions 10.0.2–10.4.1, Show does not display the points even at first.

Answer 1

I would say this is a bug, but perhaps not so unexpected.

It is indeed about having way too many points out of Range. Fixed, e.g., by selecting only the points you want to plot:

    (p1 = Plot[{Abs[5 x], -Abs[x/5]}, {x, -2, 2}, PlotRange -> {-2, 2}]) //
       StylePrint;
    zz[{x_, y_}] := Piecewise[{{{3/5 x - y + 32/100, x}, -1/5 Abs[x] <= y <= 
                    5 Abs[x]}}, {4/5 x + y + 52/100, x}];
    (p2 = ListPlot[Select[NestList[zz, {.384, .384}, 212], #.# < 4 &], 
         PlotRange -> {{-2, 2}, {-2, 2}}]) // StylePrint;
    p3 = Show[p1, p2]

yielding: