exploring complex functions

Here you can freely explore phase portraits of complex functions. Variables accessible in the freely editable formula are $z$, $A$, $B$, $C$, $D$, $a$,$b$,$c$,$d$ and $e$ where $a,b,c,d$ depend on the position of the colored points $A,B,C,D$. The dependence is ( a=z-A, b=z-B, c=z-C, d=z-D. ) Here $z$ is the location in the image. Variable $e$ is a real scalar that can be adjusted between $-1$ and $+1$.