Dragon curve in python using turtle graphics

Question

I tried making a dragon curve generator using an L-system but my generator crosses itself which is not supposed to happen in a proper dragon curve,any idea why?

import turtle
from random import randint

#turtle initialization
t = turtle.Turtle()
t.hideturtle()
t.speed(0)
turtle.delay(0)

#L-system set up
start = "fx"
rules = {'x':'x+yf+','y':'-fx-y','f':'f','+':'+','-':'-'}

while True:

    #makes a random color
    t.pencolor('#%02x%02x%02x' % (randint(0,255),randint(0,255),randint(0,255)))

    #makes a new generation of the L-system
    new = ""
    for i in start:
        new += rules[i]

    #applies the rules from text to graphics
    for i in new:
        if i == '+':
            t.right(90)
        elif i == '-':
            t.left(90)
        elif i == 'f':
            t.forward(5)
    start = new

Answer 1

It took a review of other dragon implementations to understand this. My belief is the problem is your generations aren't supposed to be additive -- each is a complete replacement for the previous. To get the effect you want, we need to strip the previous generation off the front of the current one before continuing to draw:

from turtle import Turtle, Screen, mainloop
from random import random

# L-system set up
START = "fx"
RULES = {'x':'x+yf+', 'y':'-fx-y', 'f':'f', '+':'+', '-':'-'}

LEVEL = 13

screen = Screen()
screen.tracer(False)

# turtle initialization
turtle = Turtle(visible=False)

sub_string = string = START

for _ in range(LEVEL):

    # make a random color
    turtle.pencolor(random(), random(), random())

    # apply the RULES from text to graphics
    for character in sub_string:
        if character == '+':
            turtle.right(90)
        elif character == '-':
            turtle.left(90)
        elif character == 'f':
            turtle.forward(5)

    screen.update()

    # make a new generation of the L-system
    full_string = "".join(RULES[character] for character in string)

    sub_string = full_string[len(string):]  # only the new information

    string = full_string  # the complete string for the next generation

screen.tracer(True)
turtle.hideturtle()

mainloop()