from multiprocessing import Pool

__author__ = 'Roland'
from PIL import Image
#size of image
imgx = 600
imgy = 400
#make image buffer
image = Image.new("RGB", (imgx, imgy))

# area of fractal
xa = -2.0
xb = 2.0
ya = -2.0
yb = 2.0

#define constants
max_iterations = 10  # max iterations allowed
step_derivat = 0.002e-1  # step size for numerical derivative
error = 5e-19  # max error allowed


# function will generate the newton fractal
def f(z):
    return z * z + complex(-0.31, 0.031)


def calc_i(t):
    x, y, zy = t[0], t[1], t[2]
    zx = x * (xb - xa)/(imgx - 1) + xa
    z = complex(zx, zy)
    i = 0
    while i < max_iterations:
        # make complex numerical derivative
        dz = (f(z + complex(step_derivat, step_derivat)) - f(z)) / complex(step_derivat, step_derivat)
        # Newton iteration see wikipedia
        z0 = z - f(z) / dz
        # stop to the error
        if abs(z0 - z) < error:
            break
        z = z0
        #I use modulo operation expression to do RGB colors of the pixels
        i += 1
    return x,y,i


if __name__ == '__main__':
    points = []
    # draw derivate fractal for each y and x
    for y in range(imgy):
        zy = y * (yb - ya) / (imgy - 1) + ya
        for x in range(imgx):
            points.append((x, y, zy))

    pool = Pool(processes=7)
    print(calc_i(points[0]))
    temp = pool.map(calc_i, points)
    results = []
    for t in temp:
        results.append(t)

    for x,y,i in results:
        image.putpixel((x, y), (i % 8 * 16, i % 4 * 32,i % 2 * 64))
    #save the result
    image.save("fractal.png", "PNG")