Using my established method for finding the derivative of the Mandelbrot series and Newton's formula for finding the roots of a function I produced this formula . In theory there a convergence towards the roots is expected , meaning that the condition for bailout happens when |x| approaches a small value . This isn't obvious with this formula , any improvements are welcome . R1Mandel(XAXIS) {;sciwiseg , Edward Montague ; ; Roots of Mset via derivative of Mset . ; ; y , derivative ; x , Mset . ; ; x = Pixel y = 1 : y= 2*x*y+1 x = x*x + Pixel x = x - (x/y) |x| < 4 }