This uses the Mandelbrot series as the base series . I used Maxima CAS to check that this iteration code was the same as that obtained via symbolic differentiation at each iteration ; they are. Two features that I noticed , firstly the 'channels' around the bulbs are filling up with 'silt' ; secondly there may now be some extra minibrots to the right of the main bulb. Overall this remains bland . Using Python I shall look at the series in more detail , however I'm not expecting much. d1iMandelbrot(XAXIS) {; Edward Montague (c) 2016 ; ; 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 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) |ed| < 10000 }