from random import randint
from PIL import Image, ImageDraw

def width_at_height(width,height,i):
    return(width+2*height-2*(i+1))

def F(x,y,z):
    return((not y and z) or (y and not (x and z)))

def rule110(width,height,initial=None):
    grid=[]
    for i in range(height):
        grid.append([False]*width_at_height(width,height,i))
    if(initial!=None):
        if(len(initial)==width_at_height(width,height,0)):
            grid[0]=initial
        else:
            raise f"{initial} should have length {width_at_height(width,height,0)}"
    else:
        for j in range(width_at_height(width,height,0)):
            grid[0][j] = randint(0,1)==1

    for i in range(1, height):
        for j in range(width_at_height(width,height,i)):
            grid[i][j] = F(grid[i-1][j],grid[i-1][j+1],grid[i-1][j+2])
    return(grid)


def draw_cells(grid,image_size, cell_size, true_color, false_color,output_file):
    """
    Draws a grid on an image and saves it to a file.
    
    :param image_size: Tuple (width, height) of the image
    :param cell_size: Size of each grid cell (square cells)
    :param line_color: Color of the grid lines (e.g., 'black', (255, 0, 0))
    :param output_file: Path to save the output image
    """
    # Create a blank white image
    img = Image.new("RGB", (image_size[0]*cell_size,image_size[1]*cell_size), "white")
    draw = ImageDraw.Draw(img)
    
    width, height = image_size

    
    # Draw vertical lines
    for i in range(height):
        for j in range(width):
            fill = None
            if(grid[i][j+height-1-i]):
                fill = true_color
            else:
                fill = false_color

            draw.rectangle([j*cell_size,i*cell_size,(j+1)*cell_size-1,(i+1)*cell_size-1], fill=fill)
    
    # Draw horizontal lines
    #for y in range(0, height, cell_size):
    #    draw.line([(0, y), (width, y)], fill=line_color)
    
    # Save the image
    img.save(output_file)
    print(f"Grid image saved to {output_file}")

# Parameters
width=2000
height=1000
cell_size = 1           # Cell size in pixels
line_color = "black"     # Line color for the grid
true_color = "black"
false_color ="white"
output_file ="grid.png" # Output file name

# Draw and save the grid
#draw_grid(image_size, cell_size, line_color, output_file)
initial = [False]*width_at_height(width,height,0)
initial[width_at_height(width,height,0)-height]=True
grid = rule110(width,height)
draw_cells(grid,(width,height),cell_size,true_color,false_color,output_file)