I saw this question on a mathematics telegram channel:
What does this image represent and how we can sketch it with mathematical functions or mathematical equations?
I'm not sure what this image is about and not sure what different colors mean here. I see a square divided into for equal squares. and there are lots of shapes like circle but most of them aren't really a circle. Maybe it is about some advanced fields in mathematics?
After playing around a little, I'm pretty sure that it's a domain coloring plot of the function $$ f(z) = \frac{z^2-1}{z^2+1} ,\qquad z \in \mathbf{C} , $$ with zeros at $z=\pm 1$ and poles at $z=\pm i$. (Or maybe it's $c f(z)$, or $c/f(z)$ for some constant $c$; it's impossible to tell, because the plots look basically the same with the chosen coloring.)
The plot is over the square with corners at $z = \pm 2 \pm 2i$ in the complex plane $\mathbf{C}$.
Here's my reconstruction. The colors (which aren't quite the same in my version) are based on the argument of $f(z)$, with each angle being assigned a color from a color wheel. Also, half of the shading is constructed from the argument, in such a way that each step corresponds to a change of $\pi/6$ in the argument (so 12 step for a whole lap).
And the other half of the shading is based on the absolute value of $f(z)$, with a logarithmic scale such that each step corresponds to a doubling of $|f(z)|$:
And when you stack these three pictures on top of each other, you get the final image: