Assuming that the fractal function is made inherent within the equations ed and edp the equation z=z*z+c might be removed. Using this was deflecting Newton's method from finding the basin of attraction. The new formula is somewhat faster and more intricate ; also this might provide an accurate location for the roots , I may only know once I evaluate the characteristic equation for this simple differential equation. The characteristic equation approach doesn't appear to be applicable to more complicated Differential equations. d2jbMandelbrot(XAXIS) {; Edward Montague (c) 2017 c = Pixel z = c : ed = -sin(z^2+c)+3*z^6+9*c*z^4+4*z^3+9*c^2*z^2+3*c*z^2+4*c*z+3*c^3+3*c^2 edp = -2*z*cos(z^2+c)+18*z^5+36*c*z^3+12*z^2+18*c^2*z+6*c*z+4*c z = z - ed/edp .0001 < |ed| } test { reset=2004 type=formula formulafile=fractint.frm formulaname=d2jbMandelbrot corners=-2/2/-1.5/1.5 float=y maxiter=1024 inside=bof60 colors=@default.map }