Buddhabrot Variation

import Image
import numpy as np
from random import uniform
from math import sqrt, cos, sin, pi

WIDTH, HEIGHT = 800, 800
directory = 'C:/PythonWorkspace/Images/GateAnimation/RotX'

a, b, c = 1.0, 1.0, 1.0     #Coefficients
period = 600                #Period of transform
epsilon = 2 * pi / period   #Small value to transform by
iterations = 600            #Number of series terms to sum
points = 2000000            #Number of randomly chosen test points
escapeRadius = 2.0          #"Bailout radius" for determining if C diverges
imagShift, realShift = 0.0, 0.3     #Shift view of complex plane
ratioReal, ratioImag = WIDTH / 2.8, HEIGHT / 2.8   #Screen:C-plane ratio

for n in xrange( period ):
    counters = np.zeros( ( WIDTH, HEIGHT ) )
    img = Image.new( 'RGB', ( WIDTH, HEIGHT ), ( 200, 200, 200 ) )

    a = a                                           #Transform coefficients
    b = b * cos( epsilon  ) - c * sin( epsilon )
    c = b * sin( epsilon ) + c * cos( epsilon )

    for i in xrange( points ):
        z = 0
        path = []
        realPart = uniform( -2.4, 1.0 )
        imagPart = uniform( -1.8, 1.8 )
        C = complex( realPart, imagPart )
        for j in xrange( iterations ):
            q = z.conjugate()               #Change of variable
            z = a * q**3 + b * q**2 + c * q + C   #Generating Function
            path.extend( [ z.imag + imagShift, z.real + realShift ] )
            if abs( z ) > escapeRadius:
                while path:
                    xValue = int( path.pop() * ratioReal ) + WIDTH / 2
                    yValue = int( path.pop() * ratioImag ) + HEIGHT / 2
                    if xValue > 0 and yValue > 0:
                        if xValue < WIDTH and yValue < HEIGHT:
                            counters[ xValue ][ yValue ] += 1
                            counters[ xValue ][ -yValue ] += 1
                break

    maxCount = np.amax( counters )
    for x in xrange( WIDTH ):           #Develop image from hit counts
        for y in xrange( HEIGHT ):
            color = int( 255 * ( sqrt( counters[x][y] / maxCount ) ) )
            img.putpixel( ( y, x ), ( color / 2, color / 2, color ) )

    img.save( directory + '/frame' + str( n + 1 ) + '.bmp' )