In this instance I've used Maxima Cas to directly calculate the formula for the differential equation , using the Mandelbrot Set as the function. Again I'm using Newton's method in an attempt to find the roots of the Differential equation ; if successful then I might be able to extend this to more complicated differential equations. Parameter file test { reset=2004 type=formula formulafile=fractint.frm formulaname=d2jaMandelbrot corners=-2/2/-1.5/1.5 float=y maxiter=1024 inside=bof60 outside=0 logmap=yes colors=@chroma.map } Fractal formula . d2jaMandelbrot(XAXIS) {; Edward Montague (c) 2017 c = Pixel z = c : z=z*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| }