A fractal that's a merge between my fractal differential equation and Newton's method ; yet to be checked via Maxima CAS. I call this Garden at night. test { reset=2004 type=formula formulafile=fractint.frm formulaname=d1jMandelbrot corners=-0.15769712/0.42302879/-0.77360787/-0.33806344 float=y maxiter=1024 inside=bof60 outside=0 colors=00000000d00f00h00i00k00m0ew0fx0hx0iy0ky0mznwzpwzrxzzzz7zz6zz4zz3zz2zz0zz07z06z04z03z02z00z002000000 } d1jMandelbrot(XAXIS) {; Edward Montague (c) 2017 ; ; Mandelbrot series = z ; First Derivative of Mandelbrot Series = z1 ; Second Derivative of Mandelbrot Series = z2 ; ; Differential Equation is , diff(f(z),z) + 3*f(z)*z = sin(z) ; Actually w.r.t c , where c == Pixel. ; ; z = Pixel z1=1 z2 = 0 u = 0 edp = 0 ed = 0 z2 = 2*z*z2+2*z1^2 z1 = 2*z*z1+1 u = z z = z*z + Pixel ed = 3*z*Pixel + z1 - sin(u) edp = z2 + 3*Pixel*z1 + 3*z - cos(u) z2 = 2*z*z2+2*z1^2 z1 = 2*z*z1+1 u = z z = z*z + Pixel ed = 3*z*Pixel + z1 - sin(u) edp = z2 + 3*Pixel*z1 + 3*z - cos(u) : z2 = 2*z*z2+2*z1^2 z1 = 2*z*z1+1 u = z z = z*z + Pixel ed = 3*z*Pixel + z1 - sin(u) edp = z2 + 3*Pixel*z1 + 3*z - cos(u) z = z - ed/edp .0001 < |ed| }