import numpy as np
import matplotlib.pyplot as plt

#Create an array of points to be checked
points = np.arange(-100, 101)

#The function that checks for convergence
    #If after 100 iterations abs(var) < 2 -- return True
    #Return False otherwise
def conv(x, y):
    c = complex(x,y)
    var = c
    for i in range(100):
        if abs(var) > 2:
            return False
        var = var**2 + c
    return True

#Plots the set
for i in range(201):
    for j in range(201):
        if conv(points[i]/50, points[j]/50):
            plt.scatter(points[i]/50, points[j]/50, c = 'b', s = 1, marker = '.')
plt.xlim(-2,2)
plt.ylim(-2,2)