#ulam_spiral.py
#use ezgraphics create an image file of Ulam sprial of the primes

from math import sqrt

def is_prime(n):
    if n == 1:
        return False
    if n == 2:
        return True
    else:
        if n%2 == 0:    #even no.
            return False
        t = 3
        while t <= sqrt(n):    #odd nos. up to sqrt N
            if n%t == 0:
                return False
            t += 2         #all odds.  would be better if a list of primes, or generate them?
        return True

    
import ezgraphics 

width = int(input("Enter square width of image file: "))

win = ezgraphics.GraphicsWindow(width,width)   
img = ezgraphics.GraphicsImage(width,width)    

cycles = width // 2
r = c = cycles    #start at middle of square image
img.setPixel(r,c, 255,0,0)  #red marks the middle
n = 1    #middle is 1 ?

for sqr in range(3,2*cycles+3,2):
    r = r - 1   #go up
    n += 1
    if is_prime(n):
        img.setPixel(r,c, 0,0,0)
    else:
        img.setPixel(r,c, 255,255,255)
        
    for left in range(1,sqr-1):   #sqr-2 times
        c = c - 1
        n += 1
        if is_prime(n):
            img.setPixel(r,c, 0,0,0)
        else:
            img.setPixel(r,c, 255,255,255)        
        #img.setPixel(r,c, 255,0,0)   
    for down in range(1,sqr):     #sqr-1 times
        r = r + 1
        n += 1
        if is_prime(n):   #inefficient...
            img.setPixel(r,c, 0,0,0)
        else:
            img.setPixel(r,c, 255,255,255)
    for right in range(1,sqr):
        c = c + 1
        n += 1
        if is_prime(n):
            img.setPixel(r,c, 0,0,0)
        else:
            img.setPixel(r,c, 255,255,255)
    for up in range(1,sqr):
        r = r - 1
        n += 1
        if is_prime(n):
            img.setPixel(r,c, 0,0,0)
        else:
            img.setPixel(r,c, 255,255,255)

print("n",n,"r",r,"c",c)

img.save("ulam_spiral.gif","gif")