The Chaos Game rpinki 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 is cailhe Cahword wolfram.cosive The general (n, r) chaos game begins with a polvgon 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 The Chaos Game rpinki 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 is cailhe Cahword wolfram.cosive The general (n, r) chaos game begins with a polvgon 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
