Random Walker

random_walker.py

"""
randomwalker.py
(C) Theo Patt <theo@theopatt.com>

The RandomWalker emulates, surprise suprise, a random walk.
The random walker turns either left or right (50/50) and then
"walks" one unit in that direction.

Assignment: https://www.edmodo.com/post/434660789
"""

import math
import random
import itertools

import matplotlib.pyplot as plt

class RandomWalker(object):
    def __init__(self):
        self.heading = 0
        self.start = [0, 0]
        self.position = list(self.start)
        self.history = [self.start]

    def step(self):
        turn = random.choice([1, -1])
        if self.heading in [0, 2]:
            self.position[0] += turn
        else:
            self.position[1] += turn

        self.heading += turn
        self.heading %= 4
        self.history.append(list(self.position))

    def distance(self):
        return math.sqrt((self.position[0] - self.start[0]) ** 2 +
            (self.position[1] - self.start[1]) ** 2)

    def plot_history(self):

        def pairwise(l):
            a, b = itertools.tee(l)
            next(b, None)
            return itertools.izip(a, b)

        def draw_arrow(A, B):
            plt.arrow(A[0], A[1], B[0] - A[0], B[1] - A[1],
                head_width=0.2, length_includes_head=True)

        history = self.history

        x = map(lambda v: v[0], history)
        y = map(lambda v: v[1], history)

        plt.scatter(x, y)

        for a, b in pairwise(history):
            draw_arrow(a, b)

        plt.show()

def main():
    for n_steps in xrange(0, 101):
        distances = []

        for i in xrange(50000):
            walker = RandomWalker()
            for i in xrange(n_steps):
                walker.step()

            # To view a graph of the walk, uncomment the following line
            #walker.plot_history()

            distances.append(walker.distance())

        print n_steps, sum(distances)/len(distances)

if __name__ == '__main__':
    main()