koch.py

# generates the nth iteration of the koch snowflake and outputs
# it for use in LaTeX / tikz
# sources the iteration count from the args or defaults to 0
# you could easily modify it to request a default with
# iterations = int(prompt("iterations? ") or something

import sys

# get the first numeric argument for our iteration count
iterations: int

for arg in sys.argv:
    try:
        iterations = int(arg)
        break
    except ValueError:
        pass

try:
    iterations = max(iterations, 0)
except NameError:
    iterations = 0

print("""\\begin{tikzpicture}
\t\\draw (0, 0)""", end="")

angle: int = 0
move_length = 1 / 3 ** (iterations - 1)

def turn(rel_angle):
    global angle
    angle += rel_angle

# format: -- ++(angle:length)

def move(rel_angle=angle, length=move_length):
    global angle
    angle += rel_angle
    print("\n\t-- ++(" + str(angle) + ":" + str(length) + ")", end="")

def once(depth):
    if depth > 0:
        # recurse
        # f-f++f-f
        once(depth - 1)
        turn(60)
        once(depth - 1)
        turn(-120)
        once(depth - 1)
        turn(60)
        once(depth - 1)
    else:
        # base case / 0 iterations
        move()

# axiom: f++f++f
# f → f-f++f-f
for i in range(0, 3):
    once(iterations)
    turn(-120)

print("""\n\t-- cycle;
\\end{tikzpicture}""")