How can I make ring from Gaussian distribution

I saw the formula for making a ring from Gaussian on https://arxiv.org/pdf/1606.05908.pdf but it did not work, and I found another formula which makes sphere(ring) from normal distribution

it is maked by using GCN. I used this algorithm to make a ring from a normal distribution but it also did not work.

please help me

The first example works just fine. Here's the relevant python code:

import matplotlib.pyplot as plt
import numpy as np

# Create and plot multivariate normal distribution
mean = [0, 0]
cov = [[1,0],[0,1]]
x, y = np.random.multivariate_normal(mean, cov, 100).T
plt.figure(1)
plt.plot(x, y, 'x')
plt.axis('equal')

# Generate z    
def g(xy):
    res_z = []
    for z in xy:
        z = np.array(z)
        res_z.append(z / 10 + z / np.linalg.norm(z))
    return res_z
xy = zip(x, y)
res_z = g(xy)

# Plot z
zx, zy = zip(*res_z)
plt.figure(2)
plt.plot(zx, zy, 'x')
plt.axis('equal')
plt.show()

and this outputs (if you click and drag the figures to the position shown below):

Note that when you run the script, your output will be slightly different, since np.random.multivariate_normal is doing random sampling from the underlying distribution (mean [0,0], identity covariance matrix).

I'm on Anaconda 5.1.0, Python 3.6.

HTH.