import math
import random

lr2rl = str.maketrans({'L': 'R', 'R': 'L'})

def dragon_curve(n):
    if n == 0:
        return ""
    return dragon_curve(n - 1) + "L" + dragon_curve(n - 1)[::-1].translate(lr2rl)

def turtle_graphics(f, x, y, step, turns):
    dx, dy = step, 0
    for turn in turns + "F":
        svg_line = f'<line x1="{x}" y1="{y}" x2="{x + dx}" y2="{y + dy}" stroke="black" stroke-width="3"/>'
        print(svg_line, file=f)
        x += dx; y += dy
        matrix = moves[turn]
        dx, dy = matrix[0] * dx + matrix[1] * dy, matrix[2] * dx + matrix[3] * dy

def random_turn(dx, dy):
    alpha = random.random() * 2 * math.pi
    return dx * math.cos(alpha) + dy * math.sin(alpha), -dx * math.sin(alpha) + dy * math.cos(alpha)

moves = {
    'F': (1, 0, 0, 1),
    'L': (0, 1, -1, 0),
    'R': (0, -1, 1, 0),
    'M': (math.cos(math.pi / 16), math.sin(math.pi / 16), -math.sin(math.pi / 16), math.cos(math.pi / 16))
}
f = open("generated.svg", "w")
print("<!-- Generated -->", file=f)
# os.system("generated.svg")
hei = 800
wid = 800
print('<svg xmlns="http://www.w3.org/2000/svg" height="' + str(hei) + 'px" width="' + str(wid) + 'px">', file=f)
turns = dragon_curve(13) # "FFFFLRFFFFMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM"
print(turns)
turtle_graphics(f, wid // 2, hei // 2, 3, turns)
print('</svg>', file=f)
f.close()

/*
1   L   1   v←
2   L   10  ←
3   R   11  v
4   L   100 ←
5   L   101 v
6   R   110
7   R   111 v
8   L   1000    ←
9   L   1001    v
10  L   1010
11  R   1011    v
12  R   1100
13  L   1101    v
14  R   1110
15  R   1111    v
16  L   10000   ←
17  L   10001   v
18  L   10010
19  R   10011   v
20  L   10100
21  L   10101   v
LLRLLRRLLL
10010110101110000   x
10010110101101111   x - 1
00000000000011111   x xor (x - 1)
00000000000100000   x xor (x - 1) + 1
00000000000100000   x and (x xor (x - 1) + 1) является ли 0