Sierpinski Pentagon with Python Turtle

3 thoughts on “Sierpinski Pentagon with Python Turtle”

1. Why could I never get these to stick together. they always have a gap.

   import turtle
   import random
   import math
   turtle.speed(0)
   turtle.tracer(0,0)
   turtle.hideturtle()
   turtle.up()
   def draw_pentagon(x,y,size,angle):
   turtle.up()
   turtle.goto(x,y)
   turtle.left(90)
   turtle.fd(math.cos(36)*size)
   turtle.left(90)
   turtle.fd(math.sin(36)*size)
   turtle.seth(angle)
   turtle.down()
   for i in range(5):
   turtle.fd(size)
   turtle.left(72)

   def draw_pentagon_recursion(x,y,size,angle,n):
   if n==0:
   return
   for angle in range(0,360,72):
   turtle.up()
   turtle.goto(x,y)
   turtle.seth(angle)
   draw_pentagon(x,y,size,angle)
   cx=turtle.xcor()
   cy=turtle.ycor()
   draw_pentagon_recursion(x,y,size,angle,n-1)
   angle=0
   for i in range(5):
   draw_pentagon_recursion(0,0,100,angle,5)
   angle+=252
   turtle.update()

   1. Your draw_pentagon() function has a couple of errors:

      math.cos(36) needs to be changed to math.cos(math.radians(36))

      Also the side length of the pentagon is no longer ‘size’, it should be 2*math.sin(math.radians(36))*size (some geometry work needed)

      So this is the correct draw_pentagon() function (that should align perfectly):
      def draw_pentagon(x,y,size,angle):
      turtle.up()
      turtle.goto(x,y)
      turtle.dot()
      turtle.seth(angle)
      turtle.left(90)
      turtle.fd(math.cos(math.radians(36))*size)
      turtle.dot(‘blue’)
      turtle.left(90)
      turtle.fd(math.sin(math.radians(36))*size)
      turtle.dot(‘red’)
      turtle.seth(angle)
      turtle.down()
      for i in range(5):
      turtle.fd(2*math.sin(math.radians(36))*size)
      turtle.left(72)

      You also have some problems in the draw_pentagon_recursion(). Try to fix it!

2. this is what I get. Can someone help?

   import turtle
   import colorsys
   import math
   turtle.speed(0)
   turtle.hideturtle()
   turtle.tracer(0,0)
   def draw_circle(x,y,size,color):
   turtle.up()
   turtle.seth(0)
   turtle.goto(x+math.sin(36)*size/2,y+math.sin(36)*size/2)
   turtle.down()
   turtle.fillcolor(color)
   turtle.begin_fill()
   for i in range(5):
   turtle.fd(size)
   turtle.left(72)
   turtle.end_fill()

   def draw_circle_snowflake(x,y,size,color,angle,n):
   if n==0:
   return
   draw_circle(x,y,size,color)
   h=0
   for angle in range(0,360,72):
   turtle.up()
   turtle.goto(x,y)
   turtle.seth(angle+18)
   turtle.fd(2*size)
   cx=turtle.xcor()
   cy=turtle.ycor()
   color=colorsys.hsv_to_rgb(h,1,1)
   draw_circle_snowflake(cx,cy,size/2.3,color,5*angle,n-1)

   for angle in range(360):
   draw_circle_snowflake(0,0,100,’orange’,angle,4)
   angle+=72
   turtle.update()

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