Various routines for examining the Mandelbrot series , some of these generate a rather bland image . This isn't necessarily a bad thing as this might mean that we are taming the chaotic nature of the initializing fractal. d1Mandelbrot(XAXIS) {; Edward Montague ; First Derivative of Mandelbrot Series. x = Pixel z = 1 : z = 2*x*z+1 x = x*x + Pixel |z| < 1000000 } p1Mandelbrot(XAXIS) {; Edward Montague ; Phase of Mandelbrot Series. x = Pixel y = 1 : y = 2*x*y+1 z = y/x x = x*x + Pixel |z| < 1000000 } i1Mandelbrot(XAXIS) {; Edward Montague ; First normalized summation of Mandelbrot Series. z = Pixel s = 0 n = 1 : z = z*z+Pixel s = s+z u = s/n n=n+1 |u| < 4 } f1Mandelbrot(XAXIS) {; Edward Montague ; First summation of function 1 using Mandelbrot Series. z = Pixel s = 0 n = 1 : z = z*z+Pixel s = s+sin(z) u = s/n n=n+1 |u| < 0.5 }