import math
import random
import turtle

#Parameters
X = 100
Y = 100
T = 20
L = 5 / 6 * T
N = 213

axes = ()


def settings():
	"""Turtle settings"""
	turtle.title("de Buffon's needle")
	turtle.setworldcoordinates(-(X + 2), -(Y), X + 2, Y)
	turtle.hideturtle()
	turtle.speed(0)


def go(x, y):
	"""Move cursor to the point (x, y) without drawing a line."""
	turtle.pu()
	turtle.goto(x, y)
	turtle.pd()


def parquet(t):
	"""Draw parquet's axes."""
	global X, axes
	go(-X, -Y)
	for x in range(-X, X + 1, t):
		axes += x,
		turtle.lt(90)
		turtle.goto(x, Y)
		go(x, -Y)
		turtle.rt(90)
		go(x + t, -Y)


def needle(l):
	"""
	Throw a needle.
	If it crosses the axes it colors red and returns 1,
	otherwise it returns 0.
	"""
	go(random.uniform(-X, X), random.uniform(-Y, Y))
	x1 = turtle.xcor()
	turtle.lt(random.uniform(0, 360))
	turtle.fd(l)
	x2 = turtle.xcor()
	for x in axes:
		if (x1 < x < x2) or (x2 < x < x1):
			turtle.pencolor("red")
			turtle.bk(l)
			turtle.pencolor("black")
			return 1
	else:
		return 0

settings()
parquet(T)
p = 0
for i in range(N):
	p += needle(L)
	try:
		π = (2 * L) / (T * p / N)
	except ZeroDivisionError:
		π = 0
	print(π)

print("Deviation:", abs(100 - (π / math.pi * 100)), "%")
turtle.mainloop()