Pyton 3 code
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# Newton's method valley landscape generation as a whole
# (Matplotlib Mesh plot)
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import matplotlib.pyplot as plt      # import matplotlib modules
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.figure as fg
from matplotlib import cm    # import color maps module
import numpy as np    # import numpy module

fig = plt.figure()    # set 3D figure environment
ax =  fig.add_subplot(111, projection='3d')
ax.view_init(azim=-140,elev=45)  # set view orientation
ax.dist = 3.0  # set viewpoint distance
ax.set_facecolor([1.0,.6,.15])  # set ground color

n = 8     # set number of cycles
dx = 0.0    # set initial x parameter shift
dy = 0.0    # set initial y parameter shift
L = 1.3   # set square area side
M = 300  # set side number of pixels

def f(Z):     # def scale damping of the depth function
    return np.e**(-np.abs(Z))

x = np.linspace(-L+dx,L+dx,M)      # x variable array
y = np.linspace(-L+dy,L+dy,M)      # y variable array
X,Y = np.meshgrid(x,y)    # square area grid
Z = X + 1j*Y   # complex plane area

for k in range(1,n+1):     # recursion cycle
   ZZ = Z - (Z**4 + 1)/(4*Z**3)
   Z = ZZ
   W =  f(Z)

ax.set_xlim(dx-L,dx+L)    # set x axis limits
ax.set_zlim(dy-L,dy+L)    # set y axis limits
ax.set_zlim(-3.5*L,4*L)    # set z axis limits
ax.axis("off")   # do not plot axes
ax.plot_surface(X, Y, W, rstride=1, cstride=1, cmap='flag')   # plot surface as a whole
plt.show()     # show plot