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# 15.25 (Tkinter: Koch snowflake fractal ) Section 15.8 presented the Sierpinski triangle
# fractal. In this exercise, you will write a program to display another fractal,
# called the Koch snowflake, named after a famous Swedish mathematician. A
# Koch snowflake is created as follows:
# 1. Begin with an equilateral triangle, which is considered to be the Koch fractal
# of order (or level) 0, as shown in Figure 15.14a.
# 2. Divide each line in the shape into three equal line segments and draw an outward
# equilateral triangle with the middle line segment as the base to create a
# Koch fractal of order 1, as shown in Figure 15.14b.
# 3. Repeat Step 2 to create a Koch fractal of order 2, 3, ..., and so on, as shown in
# Figure 15.14c–d.
import math
from tkinter import * # Import tkinter
class KochSnowFlake:
def __init__(self):
window = Tk() # Create a window
window.title("Koch SnowFlake") # Set a title
self.width = 600
self.height = 600
self.canvas = Canvas(window,
width=self.width, height=self.height)
self.canvas.pack()
# Add a label, an entry, and a button to frame1
frame1 = Frame(window) # Create and add a frame to window
frame1.pack()
Label(frame1,
text="Enter an order: ").pack(side=LEFT)
self.order = StringVar()
entry = Entry(frame1, textvariable=self.order,
justify=RIGHT).pack(side=LEFT)
Button(frame1, text="Display Koch SnowFlake",
command=self.display).pack(side=LEFT)
window.mainloop() # Create an event loop
def display(self):
self.canvas.delete("line")
# p1 = [self.width / 2, 100]
# p2 = [100, self.height - 100]
# p3 = [self.width - 100, self.height - 100]
p1 = [self.width / 2, self.height-165]
p2 = [100, 160]
p3 = [self.width-100, 160]
self.displayKochSnowFlake(int(self.order.get()), p1, p2)
self.displayKochSnowFlake(int(self.order.get()), p2, p3)
self.displayKochSnowFlake(int(self.order.get()), p3, p1)
def displayKochSnowFlake(self, order, p1, p2):
if order == 0: # Base condition
# Draw a triangle to connect three points
self.canvas.create_line(
p1[0], p1[1], p2[0], p2[1], tags="line")
else:
# Get points x, y, z on the edge
deltaX = p2[0] - p1[0]
deltaY = p2[1] - p1[1]
x = [p1[0] + deltaX / 3, p1[1] + deltaY / 3]
y = [p1[0] + deltaX * 2 / 3, p1[1] + deltaY * 2 / 3]
z = [((p1[0] + p2[0]) / 2 - math.cos(math.radians(30)) * (p1[1] - p2[1]) / 3),
(int)((p1[1] + p2[1]) / 2 - math.cos(math.radians(30)) * (p2[0] - p1[0]) / 3)]
# Recursively display snow flakes on lines
self.displayKochSnowFlake(order - 1, p1, x)
self.displayKochSnowFlake(order - 1, x, z)
self.displayKochSnowFlake(order - 1, z, y)
self.displayKochSnowFlake(order - 1, y, p2)
KochSnowFlake() # Create GUI
