Question

A random walk is a particular kind of probabilistic (pseudo-random) simulation that models certain statistical systems, such as Brownian motion of particles or molecules. Coin flipping is an example of a one-dimensional random walk--one dimensional because you only can go forward (when you flip heads) or backward (when you flip tails) along a straight line. Suppose you take a random walk of nsteps. How many steps away from your starting point would you expect to end up on average, if you repeated the experiment many times? Now suppose we make it two-dimensional. Suppose you can go forward, backward, left and right. How many steps away from your starting point would you expect to end up on average, if you repeated this experiment many times? And finally, suppose instead of just four choices, we could go one unit step any direction? We can generate a random direction using an angle from the x axis and move one step. Your program should take the number of steps and number of trials as input. Assume the walker always starts at 0,0 in the middle of an infinite-unit grid for any given walk. One walk == one trial. Create a graphical program that will put a dot on the grid where the walker ends each walk. At the end, print out the number of steps, number of trials, straight-line distance and actual distance traveled to the console or GUI. Display values to 3 decimal places.

import math
import random
import turtle

#function to calculate the distance between 2 points
def distance(x1, y1, x2, y2):
dx = x1 - x2;
dy = y1 - y2;
dist = math.sqrt(dx * dx + dy * dy);
return dist

def main():

#prompt and get the number of steps
steps = int(input('How many steps? '))
trails = int(input("how many trails?"))
  
#initialize
x1 = 0
y1 = 0
actualDistance = 0
s = turtle.Screen()
t = turtle.Turtle()
t.color('red')

#iterate for no.of steps specified
for k in range(steps):
#use formula to get next values
angle = random.random() * 2 * math.pi
x2 = x1 + math.cos(angle)
y2 = y1 + math.sin(angle)
trails =
#print('(%d, %d)' % (x2, y2))
actualDistance = actualDistance + distance(x1, y1, x2, y2)
t.left(angle) #turn the tutle
t.goto(x2, y2) #goto new location
x1 = x2
y1 = y2
  
  
  
#calcuate the straightline distance between origin and final position
straightDistance = distance(0, 0, x1, y1)
print('Actual distance is %.2f and straight line distance is %.2f' % (actualDistance, straightDistance))
  
s.exitonclick()

if __name__ == "__main__":
main()
I used this code, but I need to find out about how many trails.

Answer 1

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