6-Line Snowflake Fractal with Python and Turtle (Tutorial and Source Code)

Use recursion to draw the following snowflake shape generated from 6 sub-fractals of splitting lines.

The following figures show recursion depths ranging from 0 to 4.

Solution:

To solve this problem, you want to start from a function that draws a line given starting point (x,y), length, direction, and pensize. The following is the code for this function:

def line(x,y,length,direction,pensize):
  turtle.up()
  turtle.pensize(pensize)
  turtle.goto(x,y)
  turtle.down()
  turtle.seth(direction)
  turtle.fd(length)

Now you can define the recursive function that keeps branching out the shorter pair of lines. The starting point of the branch is about 2/5 of way from the original starting point. One branch is turning right about 25 degrees and the other branch is turning left about 25 degrees. Pen size should decrease proportionally too. The following is the code for this function:

def line_fractal(x,y,length,direction,pensize,n):
  if n==0: return
  line(x,y,length,direction,pensize)
  line_fractal(x+math.cos(direction*math.pi/180)*length*2/5,
               y+math.sin(direction*math.pi/180)*length*2/5,
               length*3/5,
               direction-25,
               pensize*3/5,
               n-1)
  line_fractal(x+math.cos(direction*math.pi/180)*length*2/5,
               y+math.sin(direction*math.pi/180)*length*2/5,
               length*3/5,
               direction+25,
               pensize*3/5,
               n-1)

The last function is the easiest. Just call the function above 6 times with 6 evenly spaced lines across 360 degrees. The following is the complete code for this project:

import turtle
import math

screen = turtle.Screen()
screen.title('6 Line Snowflake Fractal - PythonTurtle.Academy')
screen.setup(1000,1000)
screen.tracer(0,0)
turtle.hideturtle()
turtle.speed(0)

def line(x,y,length,direction,pensize):
  turtle.up()
  turtle.pensize(pensize)
  turtle.goto(x,y)
  turtle.down()
  turtle.seth(direction)
  turtle.fd(length)

def line_fractal(x,y,length,direction,pensize,n):
  if n==0: return
  line(x,y,length,direction,pensize)
  line_fractal(x+math.cos(direction*math.pi/180)*length*2/5,
               y+math.sin(direction*math.pi/180)*length*2/5,
               length*3/5,
               direction-25,
               pensize*3/5,
               n-1)
  line_fractal(x+math.cos(direction*math.pi/180)*length*2/5,
               y+math.sin(direction*math.pi/180)*length*2/5,
               length*3/5,
               direction+25,
               pensize*3/5,
               n-1)

def snowflake():
  for i in range(6):
    line_fractal(0,0,400,i*60,5,5)

snowflake()
screen.update()