#halving_root2.py
# 1xRoot2, chop of unit square, spiral down. Cf. A-series paper.

import math

from ezgraphics import GraphicsWindow

width = int(input("Enter width of graphics window: "))
height = width / 1.41421356

win = GraphicsWindow(width,height)   #create a drawing window
canvas = win.canvas()               

x_left = 1
x_right = width
y_down = 1
y_up = height

canvas.drawRectangle(0,0,width-1,height-1)
x = y = 0

for i in range(1,2*int(math.log2(width))):
    if i%2 == 1:
        if i%4 == 1:  #1,5,9,...
            x_left += int((x_right-x_left) / 1.41421356)
            canvas.setColor("black")
            canvas.drawLine(x_left,y_down, x_left,y_up)
            canvas.setColor("yellow")
            canvas.drawLine(x,y, x_left,y_up)
            x = x_left
            y = y_up
        else:         #3,7,11,...
            x_right -= int((x_right-x_left) / 1.41421356)
            canvas.setColor("black")
            canvas.drawLine(x_right,y_down, x_right,y_up)
            canvas.setColor("yellow")
            canvas.drawLine(x,y, x_right,y_down)
            x = x_right
            y = y_down
    else:
        if i%4 == 2:  #2,6,10,...
            y_up += int((y_down-y_up) / 1.41421356)
            canvas.setColor("black")
            canvas.drawLine(x_left,y_up, x_right,y_up)
            canvas.setColor("yellow")
            canvas.drawLine(x,y, x_right,y_up)
            x = x_right
            y = y_up
        else:         #4,8,12,...
            y_down -= int((y_down-y_up) / 1.41421356)
            canvas.setColor("black")
            canvas.drawLine(x_left,y_down, x_right,y_down)
            canvas.setColor("yellow")
            canvas.drawLine(x,y, x_left,y_down)
            x = x_left
            y = y_down

    #print(x_left,x_right,"  ",y_down,y_up)
    print("(1/root2)^",i,"=",(1/1.41421356)**i)
    
print("Look at the graphics window")