In [30]:

    

import numpy as np
from scipy.stats import uniform
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm

def generate(size=1):
    # Generate a point uniformly distributed in the square [-1, 1] x [-1, 1]
    x = uniform.rvs(loc=-1, scale=2, size=size)
    y = uniform.rvs(loc=-1, scale=2, size=size)

    # Normalize by the distance from the origin to get a point on the unit circle
    r = np.sqrt(x**2 + y**2)
    return np.column_stack([x / r, y / r])


    

In [33]:

    

dat = generate(100000)


    

In [34]:

    

dat.shape


    

    
Out[34]:





(100000, 2)

In [35]:

    

plt.plot(dat[:,0], dat[:,1], '.')
plt.gca().set_aspect('equal')


    

In [36]:

    

plt.hist2d(dat[:,0], dat[:,1], 20, norm=LogNorm())
plt.gca().set_aspect('equal')
plt.colorbar()


    

    
Out[36]:





<matplotlib.colorbar.Colorbar at 0x119a7e128>






    

In [ ]:

    

R = 1
theta =


    

In [ ]: