In this plot, a grid is drawn marking certain points \(x+yi\) with a color (left).
Then that point is transformed, so that \(f(x+yi)\) is plotted with the same color as the original \(x+yi\) that it came from (right).
\(x=\Re(z)=c\) vertical lines are colored blue with intensity based on their distance from zero (from black/blue → white/cyan as \(x\) goes from \(0\to\infty\)). x=0 is colored dark to make it stand out.
\(y=\Im(z)=c\) horizontal lines are colored red with intensity based on their distance from zero (from black/red → white/orange as \(y\) goes from \(0\to\infty\)). y=0 is colored dark to make it stand out.
\(x+yi\) points in the domain might be mapped to the same points in the range. These may be plotted on top of each other, and some information is lost.
In better but more inaccurate cases, rounding error causes the points to be plotted next to each other, so both are visible.
Enter your function here:
\(f(z)= \) →
\(r \in\) [0,]
\(r\) scale