Random Maze Generator (Python recipe) by FB36

ActiveState Code (http://code.activestate.com/recipes/578356/)

This would have been easier to read if you used more meaningful variable names. Looks good otherwise.

This is the recursive version (so it uses a stack implicitly instead of explicitly):

# Random Maze Generator using Depth-first Search (Recursive Version)
# http://en.wikipedia.org/wiki/Maze_generation_algorithm
# FB - 20121205
import random
from PIL import Image
imgx = 512; imgy = 512
image = Image.new("RGB", (imgx, imgy))
pixels = image.load()
mx = 40; my = 40 # width and height of the maze
maze = [[0 for x in range(mx)] for y in range(my)]
dx = [0, 1, 0, -1]; dy = [-1, 0, 1, 0] # directions to move in the maze

def GenerateMaze(cx, cy):
    maze[cy][cx] = 1
    while True:
        # find a new cell to add
        nlst = [] # list of available neighbors
        for i in range(4):
            nx = cx + dx[i]; ny = cy + dy[i]
            if nx >= 0 and nx < mx and ny >= 0 and ny < my:
                if maze[ny][nx] == 0:
                    # of occupied neighbors of the candidate cell must be 1
                    ctr = 0
                    for j in range(4):
                        ex = nx + dx[j]; ey = ny + dy[j]
                        if ex >= 0 and ex < mx and ey >= 0 and ey < my:
                            if maze[ey][ex] == 1: ctr += 1
                    if ctr == 1: nlst.append(i)
        # if 1 or more available neighbors then randomly select one and add
        if len(nlst) > 0:
            ir = nlst[random.randint(0, len(nlst) - 1)]
            cx += dx[ir]; cy += dy[ir]
            GenerateMaze(cx, cy)
        else: break

GenerateMaze(0, 0)
# paint the maze
for ky in range(imgy):
    for kx in range(imgx):
        m = maze[my * ky / imgy][mx * kx / imgx] * 255
        pixels[kx, ky] = (m, m, m)
image.save("RandomMaze_" + str(mx) + "x" + str(my) + ".png", "PNG")

This version does not allow zigzag corridors, so the maze looks more conventional:

# Random Maze Generator using Depth-first Search
# http://en.wikipedia.org/wiki/Maze_generation_algorithm
# FB36 - 20130106
import random
from PIL import Image
imgx = 500; imgy = 500
image = Image.new("RGB", (imgx, imgy))
pixels = image.load()
mx = 100; my = 100 # width and height of the maze
maze = [[0 for x in range(mx)] for y in range(my)]
dx = [0, 1, 0, -1]; dy = [-1, 0, 1, 0] # 4 directions to move in the maze
color = [(0, 0, 0), (255, 255, 255)] # RGB colors of the maze
# start the maze from a random cell
cx = random.randint(0, mx - 1); cy = random.randint(0, my - 1)
maze[cy][cx] = 1; stack = [(cx, cy, 0)] # stack element: (x, y, direction)

while len(stack) > 0:
    (cx, cy, cd) = stack[-1]
    # to prevent zigzags:
    # if changed direction in the last move then cannot change again
    if len(stack) > 2:
        if cd != stack[-2][2]: dirRange = [cd]
        else: dirRange = range(4)
    else: dirRange = range(4)

    # find a new cell to add
    nlst = [] # list of available neighbors
    for i in dirRange:
        nx = cx + dx[i]; ny = cy + dy[i]
        if nx >= 0 and nx < mx and ny >= 0 and ny < my:
            if maze[ny][nx] == 0:
                ctr = 0 # of occupied neighbors must be 1
                for j in range(4):
                    ex = nx + dx[j]; ey = ny + dy[j]
                    if ex >= 0 and ex < mx and ey >= 0 and ey < my:
                        if maze[ey][ex] == 1: ctr += 1
                if ctr == 1: nlst.append(i)

    # if 1 or more neighbors available then randomly select one and move
    if len(nlst) > 0:
        ir = nlst[random.randint(0, len(nlst) - 1)]
        cx += dx[ir]; cy += dy[ir]; maze[cy][cx] = 1
        stack.append((cx, cy, ir))
    else: stack.pop()

# paint the maze
for ky in range(imgy):
    for kx in range(imgx):
        pixels[kx, ky] = color[maze[my * ky / imgy][mx * kx / imgx]]
image.save("Maze_" + str(mx) + "x" + str(my) + ".png", "PNG")

Why do you have to check every neighbor if it has only one visited neighbor? Can't we just choose a random neighbor x,y where maze[y][x]=0 , set maze[y][x] to 1 and add it the stack?