2) A fractal is a curve or geometric figure comprised of a pattern that repeats at every scale. One
approach to generating a fractal is called a chaos game. A chaos game is an algorithm in which
points are plotted iteratively according to small set of rules. After a sufficient number of points
are plotted, a pattern emerges. A section of the boundary of the Dragon Curve fractal can be
plotted in MATLAB using the chaos game approach by plotting points iteratively according to
one of the following three rules that are selected randomly with equal probability. (You will need
to look up the randi function.) Write a MATLAB script that calculates the x and y vectors, then
plots x vs y using plot(x,y,'.r'). Start with x1 = 0 and y1 = 1. Perform 50000 iterations. Hint 1:
At each iteration you'll calculate a new x and y from the old x and y. Which rule you use to
calculate the new x and y is determined by ''flipping a coin'' (randi). This coin flip happens
every iteration.
Solution
Matlab Code:
x(1)=0;
y(1)=1; % Initially setting x=0;y=1
for i=1:50000 % looping from 1 to 50000
p=randi(3); % Generating a random number 1,2 or 3 will be generated
if p==1 % Initially i=1 will be selected and it will check whether randi() generated 1,2 or 3.
x(i+1)=((x(i)-y(i))/4)-(1/2); % if randi(3) generated 1 it will come to this line
y(i+1)=((x(i)+y(i))/4)+1;
else if p==2 % if randi(3) generated 2 it will execute this loop
x(i+1)=((y(i)-x(i))/4)+(1/2);
y(i+1)=-((x(i)+y(i))/4)+1;
else if p==3 % if randi(3) generated 3 it will execute this loop and will generate x,y from
previous values
x(i+1)=((x(i)+y(i))/2)+1;
y(i+1)=((y(i)-x(i))/2);
end
end
end
end % In this way we get a vector of x,y values and now we plot them
plot(x,y,'.r')