HMC Math 181: Dynamical Systems (Spring, 2002)
Final Programming Project


As part of your final exam grade in this course, you will be required to write a MATLAB program according to the specifications given below. You will have from now until the final exam's due date to work on this project.


Program Specifications

The purpose of your program will be to draw fractals from Iterated Functions Systems. You will be implementing the randomized algorithm as described in section 5.5.3 of our text. The fractal will be the fixed "point" of the IFS F=f1 u ... u fn, where each fi is a 2x2 linear function. Your program must read in data in the nx6 format as described in the text (see section 5.4.4). The following may serve as the header/help topic of your file:

% IFSFRAC   Draws the fractal defined by an iterated function system
%    FINAL PROGRAMMING PROJECT: Math 181 (Dynamical Systems)
%    SUBMITTED BY: (Your Name Here)
%
%    IFSFRAC(M,K) draws the fractal defined by the iterated function
%    system in the matrix M.  K data points are plotted in the image.
%    M represents n 2x2 linear functions of the form f(x) = Ax+b.
%    M is an nx6 matrix containing the data for one function per row.
%    For example,
%       M = [.5 0 0 .5   0  0
%            .5 0 0 .5  .5  0
%            .5 0 0 .5 .25 .5]
%    is the three-function system defining Sierpinski's triangle.
%
%    Example:
%       ifsfrac(M,5000);

function output = fracnew(C,k)
In writing your program, you are welcome to cannibalize any previously written or provided code from this course (there are specific places where it may be in your best interest to do so). There are certain features your program must contain:


Assignment Specifications


Return to: Math 181 Main Page * Greg Levin's Page * Department of Mathematics
Email: levin@hmc.edu