COMP 208: Computers in Engineering
Fall, 2018
Assignment 5
The Mouse Chase
Integrity
These assignments are to be done individually. You can collaborate on
understanding the problem but you must write the solution individually.
Your submission might be subject to Plagiarism detection software.
Due Date
Assignment 5 is due on November 20, 2018 at exactly 11:59. The cutoff is
automated and is exactly at this time. Assignments submitted within the
next hour will be considered late. After that time they will not be accepted
at all.
Introduction
This assignment deals with a problem known as the mouse or beetle
problem. A description can be found on the web site:
http://mathworld.wolfram.com/MiceProblem.html
In the general problem, n mice start at the corners of a regular n-gon. Each
mouse travels towards its closest neighbor (in a counterclockwise direction)
at a constant speed. The paths that the mice take form spiral curves. An
animation of the pattern can be seen on the above web site. The patterns
formed for n=3, 4, 5 and 6 look like the following:
Assignment
In this assignment, you are to generate a numerical solution that determines
the path of the mice.
Write a Matlab function definition that, given the value n, returns two
vectors of length n representing the x and y coordinates of the n-gon that
you start with.
Write a Matlab script that inputs a value n and generates the coordinates of
each of the n mice as they move towards each other. You will then graph the
paths the mice take.
Methodology
Start by initializing the positions of the n mice. The positions should be
symmetric and they should all lie on the unit circle centered at the origin.
You could use two vectors of length n to represent the x- and y- coordinates
of each of the mice.
On each iteration
Each mouse should move a distance d towards its neighboring mouse.
That is, towards the closest mouse in a counterclockwise direction.
(Hint: To find the coordinates of neighbor of mouse x, you just have to
add 1 to x modulo n. You can use the Matlab ‘mod’ function)
Generate the new coordinates of each mouse.
In order the graph the function, you could store the sequence of vectors in
matrices, with each line representing the coordinates at one of the time
steps.
The iterations should be repeated until the mice are sufficiently close to each
other.
You can use a value of 0.01 for d, the distance each mouse moves at each
time step.
Test you program for at least 5 different values of n.
Requirements
Your code must meet these requirements:
The script must be written in Matlab
Use sensible variable names.
Comment and indent your code
Submit a text file with the scripts and function definitions you created.
Also submit the graphs you produced. Name your files A5_123456789
and Graphs_123456789 where 123456789 is your ID. The Graph file
should have images of all the graphs generated for the different values
of n.
If any of the above requirements is not respected you might lose marks.
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