Practice recursion

interesting staff

Draw sierpinski triangle using turtle in python. If one tries to draw the biggest triangle first, he/she will find the method has very bad extensibility since there will be too many position. The first version (it’s not good at all and I know it):

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import turtle


def single_turtle_triangle(some_turtle,length):
    position=[]
    for i in range(0,3):
         some_turtle.forward(length)
         position.append(some_turtle.pos())
         some_turtle.left(120)
    some_turtle.forward(length/2)
    position.append(some_turtle.pos())
    some_turtle.left(120)
    for i in range(0,3):
        some_turtle.forward(length/2)
        position.append(some_turtle.pos())
        some_turtle.right(120)
    
    some_turtle.setheading(0)
    some_turtle.up()
    del position[-1]
    return position

def multiple_turtle_triangle(some_turtle,recursion,length):
 
    position = single_turtle_triangle(some_turtle,length)
    turtles=[]
    n=recursion
    S=n*(n+1)*(n+2)/6-(n-1)*(n)*(n+1)/6
    for i in range(0,S):
        turtles.append(some_turtle)
        
    i=2
    for i_turtle in turtles:
        i_turtle.pu()
        i_turtle.setpos(position[i])
        i_turtle.pd()
        single_turtle_triangle(i_turtle,length/2)
        i=i+1
    print(position)

def draw_art():

    window=turtle.Screen()
    window.bgcolor("white")
 
    turtle0=turtle.Turtle()
    turtle0.shape("arrow")
    turtle0.color("red")
    turtle0.pu()
    turtle0.setpos(0,0)
    turtle0.pd()

    multiple_turtle_triangle(turtle0,2,200)
    window.exitonclick()

draw_art()

Graph:

Actually there is a traditional way to draw recursion shape like this. See koch fractals. Inspired by this, a good version of Sierpinski triangle should look like this:

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import turtle

def draw_sierpinski(length,depth,some_turtle):
    if depth==0:
        for i in range(0,3):
            some_turtle.fd(length)
            some_turtle.left(120)
    else:
        draw_sierpinski(length/2,depth-1,some_turtle)
        some_turtle.fd(length/2)
        draw_sierpinski(length/2,depth-1,some_turtle)
        some_turtle.bk(length/2)
        some_turtle.left(60)
        some_turtle.fd(length/2)
        some_turtle.right(60)
        draw_sierpinski(length/2,depth-1,some_turtle)
        some_turtle.left(60)
        some_turtle.bk(length/2)
        some_turtle.right(60)
        
def draw_art():
    window = turtle.Screen()
    turtle0 = turtle.Turtle()
    draw_sierpinski(100,3,some_turtle=turtle0)
    window.exitonclick()

draw_art()

Graph: