Maxima CAS has a few limitations , hence I now program in Python too. This code calculates the second derivative of the Mandelbrot series for an initial complex value of c . The real and imaginary components are then graphed. The first 80 values have been set to a constant so that the stable condition might be observed. File mltplotz.py --- code --- """ (c) copyright 2016 sciwise@ihug.co.nz Simple demo with multiple subplots. Derivatives of Mandelbrot series . """ import numpy as np import matplotlib.pyplot as plt n=128 x2 = np.array((np.linspace(0,n,n))) y2r = np.array((np.linspace(0,n,n))) y2i = np.array((np.linspace(0,n,n))) for i in range(n): y2r[i] = 0.0 y2i[i] = 0.0 ''' Fractal calculations . ''' c=-0.5 + 0.3j z = c z1 = 1.0 z2 = 0.0 itr=0 while ( itr < n) and (abs(z2) < 100000): z2 =2*z1*z1 +2*z2*z z1 = 2*z*z1 + 1 z = z*z+c y2r[itr] = z2.real y2i[itr] = z2.imag itr=itr+1 """ --------------------------------------------------------------------- Values after 60 iterations are of interest . """ for i in range(80): y2r[i] = 0.29 y2i[i] = 0.186 plt.subplot(2, 1, 1) plt.plot(x2, y2r, 'r.-') plt.title('Second Derivative of Mandelbrot series.') plt.xlabel('index') plt.ylabel('Real z2') plt.subplot(2, 1, 2) plt.plot(x2, y2i, 'b.-') plt.xlabel('index') plt.ylabel('Imaginary z2') plt.show() exit(0)