1. (a) Let X = [0, 1]. Consider the Iterated Function System fi( X ) = X 1 , f2 ( X ) = -X + =(1, 1) 1 , 2 f3(X) = A+ ,(1, 0). If Gn is the nth stage of the construction then Gn+1 = fi(Gn) U f2(Gn) U fa(Gn). Beginning with the unit interval sketch the next three stages of the construction and calculate the fractal/box counting dimension of the object as n -+ co. (b) Play the "chaos game" to generate N = 4000 points, starting from (To, yo) = (0.5, 0.0), from the following Iterated Function System: (0.0572 ; 0.60yr) 0