#189 Mandelbrot set using python

import numpy as np
import matplotlib.pyplot as plt
# This determines the number of colors used in the plot.
# The larger the value, the longer the script will take.
max_iterations = 50
# These parameters define the boundaries of the plot
x_min, x_max = -2.5, 1.5
y_min, y_max = -1.5, 1.5
# This parameter controls the grid spacing.  A smaller value gives better
# resolution, but the script will take longer to run.
ds = 0.002
X = np.arange(x_min, x_max + ds, ds)
Y = np.arange(y_min, y_max + ds, ds)
data = np.zeros( (X.size, Y.size), dtype='uint')
for i in range(X.size):
    for j in range(Y.size):
        x0, y0 = X[i], Y[j]
        x, y = x0, y0
        count = 0
        while count < max_iterations:
            # Update x and y simultaneously.
            x, y = (x0 + x*x - y*y, y0 + 2*x*y)
            # Exit loop if (x,y) is too far from the origin.
            if (x*x + y*y) > 4.0: break
            count += 1
        data[i, j] = max_iterations - count
plt.imshow(data.transpose(), interpolation='nearest', cmap='jet')
plt.axis('off')
plt.savefig('ex189.png', dpi=300)
plt.show()