turtle_fractal.py

def rewrite(axiom, rules, times=1):
    result = "";
    for i in range(times):
        for c in axiom:
            if c in rules:
                result += rules[c]
            else:
                result += c
        axiom = result
    return result

import turtle
t = turtle.Turtle()
t.speed(5)
t.width(3)
t.ht()
t.tracer(50)

def hilbertSize(i):
    return 2**i - 1

hilbIters = 5
lineSeg = (t.window_width()-50) / hilbertSize(hilbIters)
offset = hilbertSize(hilbIters)*lineSeg/2
t.pu()
t.goto(-offset, offset)
t.pd()

def hilbert(iteration):
    path = "A"
    newPath = ""
    while iteration > 0:
        for c in path:
            if c == 'A':
                newPath += "+BF-AFA-FB+"
            elif c == 'B':
                newPath += "-AF+BFB+FA-"
            else:
                newPath += c
        path = newPath
        newPath = ""
        iteration -= 1
    return path

def cleanPath(path):
    print(f"\tInput:\n{path}\n")
    newPath = ""
    for c in path:
        if c == 'F' or c == '+' or c == '-':
            newPath += c

    path = newPath
    newPath = ""
    print(f"\tRemoved variables:\n{path}\n")
    for i in range(0, len(path)):
        c = path[i]
        print(f"{i} : {c}")
        if c == 'F':
            newPath += c
        elif c == '+':
            if i+1 < len(path) and path[i+1] == '-':
                continue
            else:
                newPath += c
        elif c == '-':
            if i+1 < len(path) and path[i+1] == '+':
                continue
            else:
                newPath += c

    path = newPath

    if path[len(path)-1] == '-' or path[len(path)-1] == '+':
        path = path[0:len(path)-1]

    print(f"\tRemoved negated rotations:\n{path}\n")
    return path
    newPath = ""
    for c in path:
        if c == 'F' or c == '+' or c == '-':
            newPath += c

    path = newPath
    newPath = ""
    for i in range(0, len(path)):
        c = path[i]
        if c == 'F':
            newPath += c
        elif c == '+':
            if i+1 < len(path) and path[i+1] == '-':
                i += 1
            else:
                newPath += c
        elif c == '-':
            if i+1 < len(path) and path[i+1] == '+':
                i += 1
            else:
                newPath += c

    path = newPath
    if path[len(path)-1] == '-' or path[len(path)-1] == '+':
        path = path[0,len(path)-2]

    return path

def turn(ang):
    t.seth(t.heading()+ang)

def drawPath(path):
    for c in path:
        if c == 'F':
            t.fd(lineSeg)
        elif c == '+':
            turn(-90)
        elif c == '-':
            turn(90)
    t.tracer(1)


path = cleanPath(hilbert(hilbIters))
drawPath(path)