Recursion Visualization

# The Three Laws of Recursion 
# 1. A recursive algorithm must have a base case.
# 2. A recursive algorithm must change its state and move toward the base case.
# 3. A recursive algorithm must call itself, recursively.

import turtle

myTurtle = turtle.Turtle()
myWin = turtle.Screen()

# Recursion Visualization
def drawSpiral(myTurtle, lineLen):
  if lineLen > 0:
    myTurtle.forward(lineLen)
    myTurtle.right(90)
    drawSpiral(myTurtle, lineLen - 5)
    
def drawTriangle(points, color, myTurtle):
  myTurtle.fillcolor(color)
  myTurtle.up()
  myTurtle.goto(points[0][0], points[0][1])
  myTurtle.down()
  myTurtle.begin_fill()
  myTurtle.goto(points[1][0], points[1][1])
  myTurtle.goto(points[2][0], points[2][1])
  myTurtle.goto(points[0][0], points[0][1])
  myTurtle.end_fill()
  
def getMid(p1, p2):
  return ((p1[0] + p2[0]) / 2, (p1[1] + p2[1]) / 2)
  
def sierpinski(points, degree, myTurtle):
  colormap = ['blue', 'red', 'green', 'white', 'yellow', 'violet', 'orange']
  
  drawTriangle(points, colormap[degree], myTurtle)
  if degree > 0:
    sierpinski(
      [points[0], getMid(points[0], points[1]), getMid(points[0], points[2])], 
      degree - 1,
      myTurtle)
    sierpinski(
      [points[1], getMid(points[0], points[1]), getMid(points[1], points[2])], 
      degree - 1,
      myTurtle)
    sierpinski(
      [points[2], getMid(points[2], points[1]), getMid(points[0], points[2])], 
      degree - 1,
      myTurtle)      


def main():
  # Recursion Visualization
  #drawSpiral(myTurtle, 100)
  
  myPoints = [[-100, -50], [0, 100], [100, -50]]
  sierpinski(myPoints, 3, myTurtle)
  
  myWin.exitonclick()
  
main()