Lorenz Butterfly in Python

#
# Lorenz Butterfly
# GPL-3.0-or-later
# license explained at 
# https://www.gnu.org/licenses/
#
import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt

sigma = 10.0
rho = 28.0
beta = 8.0/3.0

#
# defines a system of three differential
# equations to solve
# x'(t), y'(t), z'(t)
#
def f(v, t):
    x,y,z=v
    xprime = sigma*(y-x)
    yprime = rho*x - x*z - y
    zprime = x*y-beta*z
    return np.array([xprime, yprime, zprime])
#
# times is an array of 100,000 t-values 
# to be plotted between t=0 and t=50
#
times = np.linspace(0,50,10**5)
#
# initial data: x=0, y=1, z=0
#
v0 = np.array([0.0, 1.0, 0.0])
#
# integrate the differential equation in f
# starting at v0, and calculate results at 
# the t-values in times. An array of (x,y,z)
# values (100,000 of them) will be returned
#
result = odeint(f, v0, times)
#
# transpose, to get separate arrays for x, y, and z
#
x,y,z = result.T
#
# plot x as a function of z
# you could also plot x vs. y or y vs z, 
# and it would look different
#
# this code creates a plot object internally, 
# but does not display it
#
plt.plot(x,z)
fig=plt.gcf()
#
# change file type to save to other formats, 
# or comment out to merely display
#
fig.savefig("butterfly-picture.jpeg")
#
# this line is required to display the plot on the screen
#
plt.show()