Q1) Show that the attractor A of the IFS f = { R2: (x/2, y/2), ( x+1/2, y/2), ( x/4, y+3/4 ) } is neither connected nor disconnected.
Q2) Compare the initial bifurcation cascade for f: [0,1] ->. [0,1] defined by f(x) = 27/4 μx2( 1-x) with that of the logistic family g: [0,1] ->. [0,1] defined by g(x) = 4 μx( 1-x) , where in each case μ ∈ [0,1]. Identify the parameter values for which there is a single attractive fixedpoint, and the value at which it transfers stability to an attractive 2-cycle. In each case, at which value, as the paramater increases , does the attractive 2-cycle lose its stability.