This formula was constructed after reading a pdf from Yu and Ben-Israel. Doesn't appear to generate what I expected , maybe I need to delve into this a bit more , any comments from the list might be useful. If you comment out the line p1=1 then the parameter p1 is selectable from the parameter box. Newman1(XAXIS) {; Edward Montague (c) 2017 ; ; Supposedly equivalent to the Mandelbrot Set. ; ; Ref , The Newton and Halley Methods for Complex Roots ; Lily . Yau and Adi Ben-Israel ; ; c = z = Pixel p1=1 : ed =exp(-(2*atan((2*z-1)/sqrt(4*c-1)))/sqrt(4*c-1)-(2*atan(1/sqrt(4*c-1)))/sqrt(4*c-1)) edp= -exp(-(2*atan((2*z-1)/sqrt(4*c-1)))/sqrt(4*c-1)-(2*atan(1/sqrt(4*c-1)))/sqrt(4*c-1))/(z^2-z+c) zold=z; z = z - p1*ed/edp .0001 < |z-zold| ; && |z|