Inversion
Inversion considered as a geometric transformation swaps the inside and the outside of the unit circle—so to say. (The unit circle remains fixed.) So values near zero are found far from the origin, and the numbers close to zero are mapped close to infinity.
\(f(z) = 1/\overline{z},\quad z \in \mathbb{C}(0,1)\)
Adequately on the above image the typical sharp colors of the coloring meet at the origin, and the dark purplish values can be found a bit to the outside.
\(f(z) = 1/\overline{z},\quad z \in \mathbb{C}(0,3)\)
And using this coloring one can observe the changeover of white and black (respectively light and dark) colors. We may also note that the a number and its image has the same argument. (And the product of their moduli is 1, but that is not clear to see.)