Answer
Here's a program that displays a Hilbert curve of a given order using Tkinter in Python:
from tkinter import *
class HilbertCurve:
def __init__(self, order):
self.order = order
self.side = 2 ** order
self.size = 600 // self.side
self.color = "#000000"
self.root = Tk()
self.root.title("Hilbert Curve")
self.canvas = Canvas(self.root, width=600, height=600)
self.canvas.pack()
self.draw()
def draw(self):
x, y = self.side - 1, 0
self.draw_hilbert(x, y, self.order, 0, 1)
self.root.mainloop()
def draw_hilbert(self, x, y, order, direction, sign):
if order == 0:
x0 = x * self.size
y0 = y * self.size
x1 = (x + 1) * self.size
y1 = (y + 1) * self.size
self.canvas.create_line(x0, y0, x1, y1, fill=self.color, width=2)
else:
n = 2 ** (order - 1)
if direction == 0:
self.draw_hilbert(x, y, order - 1, 0, -sign)
self.draw_hilbert(x, y + n, order - 1, 1, sign)
self.draw_hilbert(x + n, y + n, order - 1, 0, sign)
self.draw_hilbert(x + n, y, order - 1, 3, -sign)
elif direction == 1:
self.draw_hilbert(x, y, order - 1, 1, sign)
self.draw_hilbert(x + n, y, order - 1, 0, -sign)
self.draw_hilbert(x + n, y + n, order - 1, 1, sign)
self.draw_hilbert(x, y + n, order - 1, 2, -sign)
elif direction == 2:
self.draw_hilbert(x, y + n, order - 1, 2, sign)
self.draw_hilbert(x + n, y + n, order - 1, 1, -sign)
self.draw_hilbert(x + n, y, order - 1, 2, sign)
self.draw_hilbert(x, y, order - 1, 3, -sign)
else:
self.draw_hilbert(x + n, y, order - 1, 3, sign)
self.draw_hilbert(x + n, y + n, order - 1, 2, -sign)
self.draw_hilbert(x, y + n, order - 1, 3, sign)
self.draw_hilbert(x, y, order - 1, 0, -sign)
hilbert = HilbertCurve(3) # create a Hilbert curve of order 3
This program creates a HilbertCurve class that takes an order parameter and generates a Tkinter window with a canvas. The draw() method calls the draw_hilbert() method to recursively draw the Hilbert curve by dividing the current square into four smaller squares and recursively drawing each of them. The direction parameter indicates the direction of the curve, and the sign parameter determines whether to draw the curve forward or backward.
Work Step by Step
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