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# 11.36 (Simulation using Turtle: self-avoiding random walk) A self-avoiding walk in a
# lattice is a path from one point to another that does not visit the same point twice.
# Self-avoiding walks have applications in physics, chemistry, and mathematics.
# They can be used to model chainlike entities such as solvents and polymers. Write
# a Turtle program that displays a random path that starts from the center and ends at
# a point on the boundary, as shown in Figure 11.11a, or ends at a dead-end point
# (i.e., surrounded by four points that have already been visited), as shown in Figure
# 11.11b. Assume the size of the lattice is 16 * 16.
import turtle
from random import random
# Draw 16 by 16 lattice
turtle.color("gray")
x = -80
for y in range(-80, 80 + 1, 10):
turtle.penup()
turtle.goto(x, y)
turtle.pendown()
turtle.forward(160)
y = 80
turtle.right(90)
for x in range(-80, 80 + 1, 10):
turtle.penup()
turtle.goto(x, y)
turtle.pendown()
turtle.forward(160)
N = 16
# lattice = 16 * [ 16 * [False]] # Wrong, each row will get the same list, i.e., id(lattice[0]) == id(lattice[1])
lattice = [] # No points in the lattice are traversed initially
for i in range(N):
list = N * [False]
lattice.append(list)
i = (N + 1) // 2
j = (N + 1) // 2
lattice[i][j] = True # Starting point
turtle.penup()
turtle.goto(0, 0)
turtle.pendown()
turtle.setheading(0)
turtle.pensize(3)
turtle.color("black")
while i > 0 and i < N - 1 and j > 0 and j < N - 1:
if lattice[i][j + 1] and lattice[i][j - 1] and lattice[i - 1][j] and lattice[i + 1][j]:
break
r = random()
if r < .25 and not lattice[i][j + 1]:
lattice[i][j + 1] = True # Right
j += 1
turtle.setheading(0)
turtle.forward(10)
elif r < .50 and not lattice[i - 1][j]:
lattice[i - 1][j] = True # Down
i -= 1
turtle.setheading(270)
turtle.forward(10)
elif r < .75 and not lattice[i][j - 1]:
lattice[i][j - 1] = True # Left
j -= 1
turtle.setheading(180)
turtle.forward(10)
elif r < 1.00 and not lattice[i + 1][j]:
lattice[i + 1][j] = True # Up
i += 1
turtle.setheading(90)
turtle.forward(10)
turtle.hideturtle()
turtle.done()
