Your inside for loop is useless as it loops over 4 values ([1,2,3,4]) and you have 4 if
insinde it. you could have:
N = 100
arr = [(0, 0)]
for u in range(1, N):
# first corner
arr.append((u, - u + 1))
# second corner
arr.append((u, u))
# third corner
arr.append((-u, u))
# fourth corner
arr.append((-u, -u))
# Transforms [(x1, y1), (x2, y2)...] in x = (x1, x2...) y = (y1, y2...)
x, y = zip(*arr)
plt.plot(x, y)
```