cgobat/montecarlo_pi.py

## montecarlo_pi.py
with open("randomstate.pkl","rb") as picklefile:
    np.random.set_state(pickle.load(picklefile))
N = 100
trials = 50000
theta = np.linspace(0,2*np.pi,360)
fractions = np.array([])
for i in range(trials):
    points = np.array([[2*x-1,2*y-1] for [x,y] in np.random.rand(N,2)])
    C = np.array([point for point in points if point[0]**2+point[1]**2 <= 1])
    fractions = np.append(fractions, len(C)/len(points))

plt.plot(np.cos(theta),np.sin(theta),color="steelblue")
plt.scatter(*points.T, marker=".",color="darkcyan")

plt.axhline(0,color="black",alpha=0.5)
plt.axvline(0,color="black",alpha=0.5)
plt.xlim((-1,1))
plt.ylim((-1,1))
plt.gca().set_aspect('equal')
plt.show()

print("This simulation puts the value of pi at approximately",4*np.mean(fractions))

## randomstate.pkl
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	with open("randomstate.pkl","rb") as picklefile:
	np.random.set_state(pickle.load(picklefile))
	N = 100
	trials = 50000
	theta = np.linspace(0,2*np.pi,360)
	fractions = np.array([])
	for i in range(trials):
	points = np.array([[2x-1,2y-1] for [x,y] in np.random.rand(N,2)])
	C = np.array([point for point in points if point[0]2+point[1]2 <= 1])
	fractions = np.append(fractions, len(C)/len(points))

	plt.plot(np.cos(theta),np.sin(theta),color="steelblue")
	plt.scatter(*points.T, marker=".",color="darkcyan")

	plt.axhline(0,color="black",alpha=0.5)
	plt.axvline(0,color="black",alpha=0.5)
	plt.xlim((-1,1))
	plt.ylim((-1,1))
	plt.gca().set_aspect('equal')
	plt.show()

	print("This simulation puts the value of pi at approximately",4*np.mean(fractions))
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