Graphing a spiral

Question

This program is made, so it graphs a spiral with N steps. What else could I add to this program?

Can this code be improved?

import matplotlib.pyplot as plt

N = 100
arr = [(0, 0)]
x = []
y = []

for u in range(1, N):

    for i in range(1, 5):
        if i % 4 == 1:                      # first corner
            arr.append((u, - u + 1))

        elif i % 4 == 2:                    # second corner (same positive numbers)
            arr.append((u, u))

        elif i % 4 == 3:                    # third corner (same [one positive and one negative] numbers)
            arr.append((-u, u))

        elif i % 4 == 0:                    # fourth corner (same negative numbers)
            arr.append((-u, -u))

print(arr)                                  # just to easily check all coordinates

for i in arr:
    x.append(i[0])
    y.append(i[1])


plt.plot(x, y)
plt.show()

Answer 1

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)

Answer 2

Instead of redundant traversal and append to multiple lists - use an efficient generator function with further zip call to aggregate the needed x, y coords sequences:

import matplotlib.pyplot as plt


def spiral_coords_gen(n=100):
    yield 0, 0
    for i in range(1, n):
        yield i, -i + 1
        yield i, i
        yield -i, i
        yield -i, -i


x, y = zip(*spiral_coords_gen())
plt.plot(x, y)
plt.show()

The output:

Answer 3

Except for what @Cal wrote, you can get rid of the zipping as well:

N=100
x=[0]
y=[0]
for u in range(1, N):
    x += [u, u, -u, -u]
    y += [1-u, u, u, -u]

plt.plot(x, y)