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# 15.36 (Turtle: Sierpinski triangle) Rewrite Listing 15.9, SierpinskiTriangle.py, using
# Turtle.
import turtle
import math
# Draw a Sierpinski triangle with the specified order
def displayTriangles(order, p1, p2, p3):
if order == 0: # Base condition
# Draw a triangle to connect three points
drawLine(p1, p2)
drawLine(p2, p3)
drawLine(p3, p1)
else:
# Get the midpoint on each edge in the triangle
p12 = midpoint(p1, p2)
p23 = midpoint(p2, p3)
p31 = midpoint(p3, p1)
# Recursively display three triangles
displayTriangles(order - 1, p1, p12, p31)
displayTriangles(order - 1, p12, p2, p23)
displayTriangles(order - 1, p31, p23, p3)
# Draw a line between two points p1 and p2
def drawLine(p1, p2):
# Compute the distance between p1 and p2
d = distance(p1[0], p1[1], p2[0], p2[1])
if p1[0] <= p2[0]: # p2 is on the right of p1
angle = math.asin((p2[1] - p1[1]) / d)
else:
angle = -math.asin((p2[1] - p1[1]) / d) + math.pi
turtle.radians()
turtle.setheading(angle)
turtle.penup()
turtle.goto(p1[0], p1[1])
turtle.pendown()
turtle.forward(d)
turtle.setheading(0)
# Return the distance between two points
def distance(x1, y1, x2, y2):
return math.sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1))
# Return the midpoint between two points
def midpoint(p1, p2):
p = 2 * [0]
p[0] = (p1[0] + p2[0]) / 2
p[1] = (p1[1] + p2[1]) / 2
return p
def main():
p1 = [0, 125]
p2 = [-150, -125]
p3 = [150, -125]
order = eval(input("Enter an order: "))
displayTriangles(order, p1, p2, p3)
turtle.done()
main()
