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

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z^5-A^5 (1-a)*(1+a) (z-A)/(z-B) z^(1+i) z^A (sin(3*a)/sin(3*b))^(1+i) Julia set Mandelbrot set Convergence of Geometric series Newton Newton-like