Draw the Octaflake fractal with recursion and Turtle library. The following shows Octaflake in various recursion depths:
Instead of stopping the recursion by recursion depth, you can also stop the recursion when the radius becomes smaller than certain size. The following Octaflake is generated by setting the threshold for recursion by radius to 10. Now you can see all octagons has the same sizes.
Source Code:
import turtle
import math
screen = turtle.Screen()
screen.title('Octaflake Fractal - PythonTurtle.Academy')
screen.setup(1000,1000)
screen.setworldcoordinates(-1000,-1000,1000,1000)
turtle.speed(0)
turtle.hideturtle()
turtle.fillcolor('royal blue')
turtle.pencolor('steel blue')
screen.tracer(0,0)
def octagon(x,y,r): #x,y is the center
turtle.up()
turtle.goto(x,y)
turtle.seth(90)
turtle.fd(r)
turtle.left(180-135/2)
turtle.down()
turtle.begin_fill()
for _ in range(8):
turtle.fd(2*r*math.sin(math.radians(45/2)))
turtle.left(45)
turtle.end_fill()
def octaflake(x,y,r,n):
if r<10:
octagon(x,y,r)
return
r2 = r/(1+1/math.tan(math.radians(45/2)))
octaflake(x,y,r-2*r2,n-1)
direction = 90
for _ in range(8):
turtle.up()
turtle.goto(x,y)
turtle.seth(direction)
turtle.fd(r-r2)
octaflake(turtle.xcor(),turtle.ycor(),r2,n-1)
direction += 45
octaflake(0,0,900,3)
screen.update()
