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estimate_pi.py
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estimate_pi.py
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import tkinter as tk
import random
import numpy as np
REFRESH_RATE = 10
SQUARE_SIDE = 600
SQUARE_BUFFER = 100
CIRCLE_SIDE = 600
CIRCLE_BUFFER = 100
class EstimatePi(tk.Frame):
def __init__(self, parent, *args, **kwargs):
tk.Frame.__init__(self, parent, *args, **kwargs)
self.parent = parent
# Set up window
self.parent.title("Estimate Pi")
self.parent.geometry("800x800")
# Approximation
self.pi_approximation = 0
self.total_points = 0
self.total_in_circle = 0
self.error = 0
# Set up canvas
self.canvas = tk.Canvas(self.parent, height=800, width=800)
self.canvas.pack()
# Generate random points
self.setup_shapes()
# Begin chaos
self.parent.after(REFRESH_RATE, self.take_step)
def setup_shapes(self):
self.canvas.create_rectangle(
SQUARE_BUFFER,
SQUARE_BUFFER,
SQUARE_BUFFER + SQUARE_SIDE,
SQUARE_BUFFER + SQUARE_SIDE,
fill="white"
)
self.canvas.create_oval(
CIRCLE_BUFFER,
CIRCLE_BUFFER,
CIRCLE_BUFFER + CIRCLE_SIDE,
CIRCLE_BUFFER + CIRCLE_SIDE,
fill="green"
)
self.pi_text = self.canvas.create_text(
CIRCLE_BUFFER,
CIRCLE_BUFFER / 2,
text="Pi is unknown",
fill="yellow",
font=('Helvetica 15 bold'),
justify=tk.LEFT
)
self.error_text = self.canvas.create_text(
CIRCLE_BUFFER,
(CIRCLE_BUFFER / 2) + 20,
text="Error is unknown",
fill="yellow",
font=('Helvetica 15 bold'),
justify=tk.LEFT
)
def coordinate_to_plot(self, random_value, isX):
shift = (CIRCLE_SIDE / 2) + CIRCLE_BUFFER
if isX:
return shift + ((CIRCLE_SIDE / 2) * random_value)
return ((CIRCLE_SIDE / 2) * random_value) + CIRCLE_BUFFER
def vector_magnitude(self, point):
# point -> (x, y)
return np.sqrt(point[0] ** 2 + point[1] ** 2)
def update_approximation(self, vector):
magnitude = self.vector_magnitude(vector)
self.total_points += 1
if magnitude <= 1:
self.total_in_circle += 1
self.pi_approximation = 4 * (self.total_in_circle / self.total_points)
self.error = abs(((self.pi_approximation - np.pi) / np.pi)) * 100
def take_step(self):
x_coord = random.uniform(0, 1)
y_coord = random.uniform(0, 1)
vector = (x_coord, y_coord)
plot_x = self.coordinate_to_plot(vector[0], True)
plot_y = self.coordinate_to_plot(vector[1], False)
self.canvas.create_oval(
plot_x - 4,
plot_y - 4,
plot_x + 4,
plot_y + 4,
fill="red"
)
# Update our estimation
self.update_approximation(vector)
self.canvas.itemconfigure(self.pi_text, text=f"Pi is approximately {round(self.pi_approximation, 6)}")
self.canvas.itemconfigure(self.error_text, text=f"Error is {round(self.error, 6)}")
self.parent.after(REFRESH_RATE, self.take_step)
if __name__ == "__main__":
root = tk.Tk()
app = EstimatePi(root)
app.pack(side="top", fill="both", expand=True)
root.mainloop()