This is what the winding number $n(\gamma ,a)$ of curve $\gamma$ around point $a$, expressed as special case of Cauchy's integral formula looks like on potentially-non-closed loops, with complex numbers mapped to a hue-luminance space.

$$ n(\gamma ,a) = \frac{1}{2 \pi i}\int_{\gamma}^{}\frac{1}{z-a}dz $$

Demo here