The Chaos Game A very interesting method of generating a family of curves which includes the Sierpinski triangle (see http://mathworld.wolfram.com/SierpinskiSieve.html) is called the Chaos Game. This is an algorithm described by Barnsley in 1988. It is a chaotic random process that can generate orderly patterns such as the Sierpinski Triangle. The general (n, r) chaos game begins with a polygon with n vertices which lie on the unit circle. One of the vertices is selected as a starting point, call it A. Then a vertex is randomly chosen from the remaining n-1 vertices. Call it B. A point, C, is drawn on the straight line between A and B at a fraction r of the distance between A and B. After this initial computation of C, one of the n vertices is randomly selected (call it B) and a new point is drawn at a fraction r of the distance between C and B. This process is repeated many times. (See http://mathworld.wolfram.com/ChaosGame.html). When these points are plotted some of the patterns obtained for various values of n and r can be viewed on the ChaosGame web page referenced above.

Assignment:

You are to write a Matlab program to generate a sequence of points obtained by playing the chaos game with different values for n and r. You should submit the images you obtain for the values n=3, r=1/2; n=5, r=1/3; n=6, r= 1/3; n=5, r=3/8 and at least one additional pair of values. Each image should be generated using 10000 points.

Requirements Submit a Matlab function definition that generates the graph for given values of n and r. Use meaningful variable names Comment and indent your code. It is your responsibility to make it readable to the grader