Just for clarification: As it stands
In[68]:= Grid[
Join[{{"ds", "black", "white"}},
Transpose[
Join[{Range[-5, 5]},
Map[Last,
Transpose[
ImageLevels /@ (Binarize /@ (Image /@ (Draw /@
Range[-5, 5])))], {2}]]]]]
Out[68]=
ds black white
-5 640000 0
-4 640000 0
-3 489362 150638
-2 458308 181692
-1 430486 209514
0 430486 209514
1 430486 209514
2 511558 128442
3 581104 58896
4 640000 0
5 640000 0
for Abs[ds] > 3
the graphics from Draw[ds]
is uniformly black. An infinite zoom cannot be directly observed. The pictures for
$ds \in \{-1,1,1\}$ seem to agree visually. How did
$ds$ vary in the GIF animation?
Background: I'm interested in a working example of a fractal one can zoom out, with other words iterate backwards behind the starting set or with again other words having the starting set appearing if iterating from negative iteration numbers to iteration number 0. Then going forward, i.e. zoom in. Your example seemed to deliver it, but seems to need some more work to accomplish that.