Project #1: A drunkard's walk

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CSC 220 – Project #1
Project Details:
A drunkard's walk. A drunkard begins walking aimlessly, starting at a lamp post. At each
time step, the drunkard forgets where he or she is, and takes one step at random, either
north, east, south, or west, with probability 25%. How far will the drunkard be from the
lamp post after N steps?
1. Write a program RandomWalker.java that takes a command-line argument N and
simulates the motion of a random walker for N steps. After each step, print the
location of the random walker, treating the lamp post as the origin (0, 0). Also, print
the square of the distance from the origin.
$java RandomWalker 10 $java RandomWalker 20
(0, 0) (0, 0)
(0, -1) (0, 1)
(0, 0) (-1, 1)
(0, 1) (-1, 2)
(0, 2) (0, 2)
(-1, 2) (1, 2)
(-2, 2) (1, 3)
(-2, 1) (0, 3)
(-1, 1) (-1, 3)
(-2, 1) (-2, 3)
(-3, 1) (-3, 3)
squared distance = 10 (-3, 2)
(-4, 2)
(-4, 1)
(-3, 1)
(-3, 0)
(-4, 0)
(-4, -1)
(-3, -1)
(-3, -2)
(-3, -3)
squared distance = 18
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2. Write a program RandomWalkers.java that takes two command-line argument N
and T. In each of T independent experiments, simulate a random walk of N steps and
compute the squared distance. Output the mean squared distance (the average of
the T squared distances).
% java RandomWalkers 100 100000 % java RandomWalkers 400 100000
mean squared distance = 100.15086 mean squared distance = 401.22024

% java RandomWalkers 100 100000 % java RandomWalkers 800 100000
mean squared distance = 99.95274 mean squared distance = 797.5106

% java RandomWalkers 200 100000 % java RandomWalkers 1600 100000
mean squared distance = 199.57664 mean squared distance = 1600.13064

As N increases, we expect the random walker to end up further and further away
from the origin. But how much further? Use RandomWalkers to formulate a
hypothesis as to how the mean squared distance grows as a function of N.
Use T = 100,000 trials to get a sufficiently accurate estimate.
Remark: this process is a discrete version of a natural phenomenon known as Brownian
motion. It serves as a scientific model for an astonishing range of physical processes
from the dispersion of ink flowing in water, to the formation of polymer chains in
chemistry, to cascades of neurons firing in the brain.
Readable code:
Make sure that your code is readable: use descriptive variable names. Indent your code.
Comment your code according to the commenting guidelines.
What to turn in:
JAR your *.java and *.class files into a file called Project1.jar. Upload the jar file
to Canvas under category Project1.
Hint:
Please note that you will submit two JAVA programs, RandomWalker.java and
RandomWalkers.java. You will use for loop in this project. The first program will
use a for loop to simulate the N steps. The second program will use two nested for
loops, the outer loop to simulate T trials and the inner loop to simulate N steps.
The following the is the incomplete version of RandomWalker.java. Your program can
be based on this framework.
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/**********************************************************************
*
* Programmer: your name
* Instructor: Dr. Tao
* Course: CSC220-03
* Compilation: javac RandomWalkers.java
* Execution: java RandomWalkers N
*
* Simulates how far away after N steps random walk
*
*
***********************************************************************
/
public class RandomWalker {
public static void main(String[] args) {
int N = Integer.parseInt(args[0]);
int x = 0; // starting x position
int y = 0; // starting y position
double r;
// repeat until walk N steps
int step;

}
}