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# 15.29 (Tkinter: H-tree fractal) An H-tree is a fractal defined as follows:
# 1. Begin with a letter H. The three lines of the H are of the same length, as shown
# in Figure 15.1a.
# 2. The letter H (in its sans-serif form, H) has four endpoints. Draw an H centered
# at each of the four endpoints to an H-tree of order 1, as shown in Figure 15.1b.
# These Hs are half the size of the H that contains the four endpoints.
# 3. Repeat Step 2 to create an H-tree of order 2, 3, ..., and so on, as shown in
# Figure 15.1c–d.
# Write a Python program that draws an H-tree, as shown in Figure 15.1.
import math
from tkinter import * # Import tkinter
class H_Tree:
def __init__(self):
window = Tk() # Create a window
window.title("H Tree") # 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 H tree",
command=self.display).pack(side=LEFT)
window.mainloop() # Create an event loop
def display(self):
self.canvas.delete("line")
length = 200
center = [self.width / 2, self.height / 2]
self.displayHTree(int(self.order.get()), center, length / 2)
def displayHTree(self, order, center, length):
if order >= 0:
p1 = [center[0] - length / 2, center[1] + length / 2]
p2 = [center[0] - length / 2, center[1] - length / 2]
p3 = [center[0] + length / 2, center[1] + length / 2]
p4 = [center[0] + length / 2, center[1] - length / 2]
self.canvas.create_line(
center[0] - length / 2, center[1],
center[0] + length / 2, center[1], tags="line")
self.canvas.create_line(
p1[0], p1[1], p2[0], p2[1], tags="line")
self.canvas.create_line(
p3[0], p3[1], p4[0], p4[1], tags="line")
# Recursively display three H shape of a smaller order
self.displayHTree(order - 1, p1, length / 2)
self.displayHTree(order - 1, p2, length / 2)
self.displayHTree(order - 1, p3, length / 2)
self.displayHTree(order - 1, p4, length / 2)
H_Tree() # Create GUI
