For real $x,y$, define $g(x,y)=\{x y\}$ where $\{\cdot\}$denote the fractional part.
For a point $(x,y)$ in the plane, color the point as $g(x,y)$ wherezero is black, one is white and smaller is darker.
Q1 Is there fractal pattern for $g(x,y)$ in this construction?
Experiments suggest there are patterns which persist zooming in.
Figure 1a: $g(x,y): -18.05 < x,y <18.05 $
frac_xy_(-18.05,18.05),(-18.05,18.05).png
Figure 2: $g(x,y): -18 < x,y < 18$
frac_xy_-18..18.png
One possible approach is to examine the zeros of $g(x,y)=C$for constant $C$.