Squarify

squarify.py

# Squarify
# subdivide a rectangle into squares whose sum have the same area using
# the identity:
#
#   w * h = min(w, h) ** 2 + (max(w,h) - min(w,h)) * min(w, h)

W,H = 1920, 1080

w,h = W, H
lengths = []
while True:
    if w < h:
        lengths.append(w)
        h -= w
    elif h < w:
        lengths.append(h)
        w -= h
    else:
        lengths.append(min(w, h))
        break

# [1080, 840, 240, 240, 240, 120, 120]
print(lengths)

assert sum([x*x for x in lengths]) == W * H