'''
    one simple
    iterated exponentiation ...^i^i^i 
    in complex plane
'''
import numpy as np
import matplotlib.pyplot as plt


# prepare plot and calculation
c = 0+1j        # imaginary unit
m = 5000         # points in iteration 
z = c           # starting point of iteration
#       prepare plot frame and description
plt.figure(figsize=(10,6.8))
plt.xlabel('Re',fontsize=14)
plt.ylabel('Im',fontsize=14)
plt.title('...z^z^z,   z='+str(c),fontsize=14)
plt.axis([-0.2, 1.1, -0.5, 1.2])
plt.grid(True,color=(.75,.9,.97))

#       iterate and plot points one by one
for n in range(m):      
# prepare RGB color index and line weight of the next point
    f = (n/m)**0.6;     lw = 1.*(1.05-f)
    r = f*0.5 +0.5;     g = f*0.7;      b = (1-f)*.3 + 0.1
# plot singe point
    plt.scatter(np.real(z),np.imag(z),s=6,color=(r,g,b),linewidth=lw)
    
# the iteration 
    z = c**z       # exponentiation done right (c**z, not z**c)
# break out from loop if iteration diverges, |z| > some value
    if(abs(z) > 999.): break
# after iteration, show plot on screen
plt.show()