https://www.reddit.com/r/vexillology/comments/95q6kk/us_flagsimplified/e3v8wma/?context=3

flagflag.py

# coding: utf-8

import itertools

stars = [complex(x,y) for x,y in itertools.product(range(11),range(5)) if (x + y) % 2 == 0]

def print_flag(s):
    lines = []
    for y in range(5):
        line = []
        for x in range(11):
            if complex(x,y) in s:
                line.append("*")
            else:
                line.append(" ")
        lines.append(line)
    print '┌─────────────────────┐'
    print '\n'.join('│%s│' % ' '.join(line) for line in lines)
    print '\n'.join('│%s│' % ' '.join(line) for line in lines[-2::-1])
    print '└─────────────────────┘'

flags = []

def first_connected(field, blob):
    for i in field:
        if any(1 < abs(i-star) < 2 for star in blob):
            return i
    return None

def check_flag(flag):
    centres = len([s for s in flag if s.imag == 4])
    others = len([s for s in flag if s.imag < 4])

    if centres == 0:
        return False

    if others * 2 + centres != 13:
        return False

    connected = [flag[0]]
    stars = set(flag) - set(connected)

    for i in range(1,len(flag)):
        s = first_connected(stars, connected)
        if s is not None:
            connected.append(s)
            stars = set(flag) - set(connected)
        else:
            print "not connected %s to %s" % (stars, connected)
            return False

    return True

print check_flag([0+0j,1+1j,0+2j,1+3j,0+4j,2+4j,4+4j,6+4j,8+4j])
exit(0)

for n in [9]:
    count = 0
    print "%i centre stars" % (n * 2 - 13)
    for flag in itertools.combinations(stars, n):
        if check_flag(flag):
            flags.append(flag)
            count += 1
            print_flag(flag)
    print "%i total" % count

print "%i total flags " % len(flags)