index.py

from PIL import Image
import colorsys
import math
import os

width = 100

x = -0.65
y = 0
xRange = 3.4
aspectRatio = 4/3

height = round(width / aspectRatio)
yRange = xRange / aspectRatio
minX = x - xRange / 2
maxX = x + xRange / 2
minY = y - yRange / 2
maxY = y + yRange / 2

precision = 500

img = Image.new('RGB', (width, height), color = 'black')
pixels = img.load()

def logColor(distance):
    color = -1 * math.log(distance, 50)
    rgb = colorsys.hsv_to_rgb(0.4 + 0.9 * color,0.8,0.9)
    return tuple(round(i * 255) for i in rgb)

def powerColor(distance, exp, const, scale):
    color = distance**exp
    rgb = colorsys.hsv_to_rgb(const + scale * color,1 - 0.6 * color,0.9)
    return tuple(round(i * 255) for i in rgb)

for row in range(height):
    for col in range(width):
        x = minX + col * xRange / width
        y = maxY - row * yRange / height
        oldX = x
        oldY = y
        for i in range(precision + 1):
            a = x*x - y*y #real component of z^2
            b = 2 * x * y #imaginary component of z^2
            x = a + oldX #real component of new z
            y = b + oldY #imaginary component of new z
            if x*x + y*y > 4:
                break
        if i < precision:
            distance = (i + 1) / (precision + 1)
            rgb = powerColor(distance, 0.2, 0.27, 1.0)
            pixels[col,row] = rgb
        index = row * width + col + 1
        print("{} / {}, {}%".format(index, width * height, round(index / width / height * 100 * 10) / 10))

img.save('output.png')
os.system('open output.png')