Generate julia set images.

julia_set.py

# Requires PIL

import math
  
class Complex(object):
    def __init__(self, real, img):
        self.real = real
        self.img = img
          
    def __mul__(self, comp):
        a = self.real * comp.real - self.img * comp.img
        b = self.real * comp.img + self.img * comp.real
        return Complex(a, b)
          
    def __add__(self, comp):
        a = self.real + comp.real
        b = self.img + comp.img
        return Complex(a, b)
          
    def __sub__(self, comp):
        a = self.real - comp.real
        b = self.img - comp.img
        return Complex(a,b)
          
    def __div__(self, comp):
        comp.img = -1*comp.img
        a = self.real * comp.real - self.img * comp.img + 0.0
        b = self.real * comp.img + self.img * comp.real + 0.0
           
        denominator = comp.real ** 2 + comp.img ** 2
        a /= denominator
        b /= denominator
          
        return Complex(a,b) 
      
    def __str__(self):
        if self.img > 0:
            if self.real != 0:
                return str(self.real) + "+" + str(self.img) + "i"
            else:
                return str(self.img)
        elif self.img == 0:
            return str(self.real)
        else:
            if self.real != 0:
                return str(self.real) + str(self.img) + "i"
            else:
                return str(self.img)
                  
    def __pow__(self, index):
        comp = Complex(1, 0)
        for i in xrange(index):
            comp *= self
        return comp
      
    def mod(self):
        return self.real ** 2 + self.img ** 2
          
    def arg(self):
        if self.real == 0:
            if self.img == 0:
                return 0
            else:
                return math.pi/2 * (self.img / math.fabs(self.img))
        else:
            return math.atan((1.0 * self.img) / self.real)
              
#==============================================================================#
  
import Image
 
# User definied parameters
res = int(raw_input("Input resolution: "))
c_real = float(raw_input("Input real part of c: "))
c_imag = float(raw_input("Input imaginary part of c: "))
  
# Hard coded parameters
corn_x = -2 # x co-ordinate of top left corner
corn_y = 2  # y co-ordinate of top left corner
size = 4.0  # length of square
max_iter = 100
mag_limit = 4
 
img = Image.new("RGB", (res,res), (255,255,255))
  
for i in xrange (1, res):
    for j in xrange(1,res):
        count = 0
        z = Complex(corn_x + i*size/res, corn_y - j*size/res)
        while (count < max_iter and z.mod() < mag_limit):
            count += 1
            z = z**2 + Complex(c_real, c_imag)
  
        colour = 255 - int(math.floor(count * 255 / max_iter))
        img.putpixel((i,j),(colour,colour,colour))
          
img.save("complex.png","PNG")